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Journal of Industrial & Management Optimization
October 2012 , Volume 8 , Issue 4
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2012, 8(4): 781-806
doi: 10.3934/jimo.2012.8.781
+[Abstract](2243)
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Abstract:
In this paper, we first consider single server retrial queues with two way communication. Ingoing calls arrive at the server according to a Poisson process. Service times of these calls follow an exponential distribution. If the server is idle, it starts making an outgoing call in an exponentially distributed time. The duration of outgoing calls follows another exponential distribution. An ingoing arriving call that finds the server being busy joins an orbit and retries to enter the server after some exponentially distributed time. For this model, we present an extensive study in which we derive explicit expressions for the joint stationary distribution of the number of ingoing calls in the orbit and the state of the server, the partial factorial moments as well as their generating functions. Furthermore, we obtain asymptotic formulae for the joint stationary distribution and the factorial moments. We then extend the study to multiserver retrial queues with two way communication for which a necessary and sufficient condition for the stability, an explicit formula for average number of ingoing calls in the servers and a level-dependent quasi-birth-and-death process are derived.
In this paper, we first consider single server retrial queues with two way communication. Ingoing calls arrive at the server according to a Poisson process. Service times of these calls follow an exponential distribution. If the server is idle, it starts making an outgoing call in an exponentially distributed time. The duration of outgoing calls follows another exponential distribution. An ingoing arriving call that finds the server being busy joins an orbit and retries to enter the server after some exponentially distributed time. For this model, we present an extensive study in which we derive explicit expressions for the joint stationary distribution of the number of ingoing calls in the orbit and the state of the server, the partial factorial moments as well as their generating functions. Furthermore, we obtain asymptotic formulae for the joint stationary distribution and the factorial moments. We then extend the study to multiserver retrial queues with two way communication for which a necessary and sufficient condition for the stability, an explicit formula for average number of ingoing calls in the servers and a level-dependent quasi-birth-and-death process are derived.
2012, 8(4): 807-819
doi: 10.3934/jimo.2012.8.807
+[Abstract](1820)
+[PDF](491.5KB)
Abstract:
In video streaming, feedback-based rate control is utilized for guaranteeing video quality on an end-to-end basis. This paper considers the effect of feedback-based rate controls on video quality from queueing theoretical point of view. We focus on a video streaming mechanism with a feedback-based rate control where a video server regulates the packet-sending rate according to the number of data blocks stored in a client node. The client node has two buffers: a synchronization buffer and a receiver buffer. Packets arriving to the client node are stored in the synchronization buffer first, and a video-data block is retrieved from a fixed number of packets in the synchronization buffer and forwarded to the receiver buffer. We model the client node as a discrete-time two-queue concatenated system with state-dependent packet arrivals, deriving the starvation and overflow probabilities. Numerical examples show the effectiveness of the feedback-based rate controls for improving both these probabilities. In particular, the rate control which is not sensitive to the number of data blocks in the receiver buffer makes these probabilities significantly small.
In video streaming, feedback-based rate control is utilized for guaranteeing video quality on an end-to-end basis. This paper considers the effect of feedback-based rate controls on video quality from queueing theoretical point of view. We focus on a video streaming mechanism with a feedback-based rate control where a video server regulates the packet-sending rate according to the number of data blocks stored in a client node. The client node has two buffers: a synchronization buffer and a receiver buffer. Packets arriving to the client node are stored in the synchronization buffer first, and a video-data block is retrieved from a fixed number of packets in the synchronization buffer and forwarded to the receiver buffer. We model the client node as a discrete-time two-queue concatenated system with state-dependent packet arrivals, deriving the starvation and overflow probabilities. Numerical examples show the effectiveness of the feedback-based rate controls for improving both these probabilities. In particular, the rate control which is not sensitive to the number of data blocks in the receiver buffer makes these probabilities significantly small.
2012, 8(4): 821-840
doi: 10.3934/jimo.2012.8.821
+[Abstract](1703)
+[PDF](512.9KB)
Abstract:
We consider a time slotted cognitive radio network under Rayleigh fading where multiple secondary users (SUs) contend for spectrum usage over available primary users' channels. We analyze the performance of a channel access policy where each SU stochastically determines whether to access a wireless channel or not based on a given access probability. In the analysis, we focus on the queueing performance of an arbitrary SU with the channel access policy. To improve the queueing performance of SUs, the access probability in our channel access policy is adapted to the knowledge on the wireless channel information, e.g., the number of available channels and the nonfading probability of channels. It is then important to obtain the optimal access probabilities from the queueing performance perspective.
In this paper we consider three scenarios. In the first scenario, all SUs have full information on wireless channel status and fading channel conditions. In the second scenario, all SUs have the information on wireless channel status but do not know their fading channel conditions, and in the last scenario all SUs do not have any information on wireless channel status and conditions. For each scenario we analyze the queueing performance of an arbitrary SU and show how to obtain the optimal access probabilities with the help of the effective bandwidth theory. From our analysis we provide an insight on how to design an optimal channel access policy in each scenario. We also show how the optimal channel access policies in three scenarios are related with each other. Numerical results are provided to validate our analysis. In addition, we investigate the performance behaviors of the optimal channel access policies.
We consider a time slotted cognitive radio network under Rayleigh fading where multiple secondary users (SUs) contend for spectrum usage over available primary users' channels. We analyze the performance of a channel access policy where each SU stochastically determines whether to access a wireless channel or not based on a given access probability. In the analysis, we focus on the queueing performance of an arbitrary SU with the channel access policy. To improve the queueing performance of SUs, the access probability in our channel access policy is adapted to the knowledge on the wireless channel information, e.g., the number of available channels and the nonfading probability of channels. It is then important to obtain the optimal access probabilities from the queueing performance perspective.
In this paper we consider three scenarios. In the first scenario, all SUs have full information on wireless channel status and fading channel conditions. In the second scenario, all SUs have the information on wireless channel status but do not know their fading channel conditions, and in the last scenario all SUs do not have any information on wireless channel status and conditions. For each scenario we analyze the queueing performance of an arbitrary SU and show how to obtain the optimal access probabilities with the help of the effective bandwidth theory. From our analysis we provide an insight on how to design an optimal channel access policy in each scenario. We also show how the optimal channel access policies in three scenarios are related with each other. Numerical results are provided to validate our analysis. In addition, we investigate the performance behaviors of the optimal channel access policies.
2012, 8(4): 841-860
doi: 10.3934/jimo.2012.8.841
+[Abstract](1382)
+[PDF](450.1KB)
Abstract:
We mathematically analyze the discontinuous reception (DRX), a power saving mechanism in 3GPP LTE where both downlink and uplink packet arrivals at a user equipment (UE) and an evolved node B (eNB) follow Poisson processes. We construct a 2-dimensional discrete time embedded Markov chain. We obtain the average power consumption, average downlink delay and average uplink delay. The analytical results match with the simulation results very well. We show that there is a tradeoff between the power consumption and the downlink delay, i.e., the average power consumption decreases and the average downlink delay increases as the DRX cycle increases or the inactivity time decreases. We also see that a presence of uplink packet decreases the downlink packet delay, but increases the power consumption.
We mathematically analyze the discontinuous reception (DRX), a power saving mechanism in 3GPP LTE where both downlink and uplink packet arrivals at a user equipment (UE) and an evolved node B (eNB) follow Poisson processes. We construct a 2-dimensional discrete time embedded Markov chain. We obtain the average power consumption, average downlink delay and average uplink delay. The analytical results match with the simulation results very well. We show that there is a tradeoff between the power consumption and the downlink delay, i.e., the average power consumption decreases and the average downlink delay increases as the DRX cycle increases or the inactivity time decreases. We also see that a presence of uplink packet decreases the downlink packet delay, but increases the power consumption.
2012, 8(4): 861-875
doi: 10.3934/jimo.2012.8.861
+[Abstract](2094)
+[PDF](330.5KB)
Abstract:
A single-server retrial queue with two types of customers in which the server is subject to vacations along with breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. The service times of the two types of customers have two different independent general distributions. We assume that when a service is completed, the server will take vacations after an exponentially distributed reserved time. It is assumed that the server has an exponentially distributed lifetime, a generally distributed vacation time and a generally distributed repair time. There is no waiting space in front of the server, therefore, if the server is found busy, or on vacation, or down, the blocked two types of customers form two sources of repeated customers. Explicit expressions are derived for the expected number of retrial customers of each type. Additionally, by assuming both types of customers face linear costs for waiting and retrial, we discuss and compare the optimal and equilibrium retrial rates regarding the situations in which the customers are cooperative or noncooperative, respectively.
A single-server retrial queue with two types of customers in which the server is subject to vacations along with breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. The service times of the two types of customers have two different independent general distributions. We assume that when a service is completed, the server will take vacations after an exponentially distributed reserved time. It is assumed that the server has an exponentially distributed lifetime, a generally distributed vacation time and a generally distributed repair time. There is no waiting space in front of the server, therefore, if the server is found busy, or on vacation, or down, the blocked two types of customers form two sources of repeated customers. Explicit expressions are derived for the expected number of retrial customers of each type. Additionally, by assuming both types of customers face linear costs for waiting and retrial, we discuss and compare the optimal and equilibrium retrial rates regarding the situations in which the customers are cooperative or noncooperative, respectively.
2012, 8(4): 877-894
doi: 10.3934/jimo.2012.8.877
+[Abstract](1723)
+[PDF](437.6KB)
Abstract:
Here we study large deviations in networks that are more likely to result from the accumulation of many slightly unusual events. We are particularly interested in analyzing large deviations where the most probable path changes direction. These deviations arise when a large deviation in one part of the system cascades across the network to produce a large deviation in another part of the network. Our technique involves the construction of an approximate time reversal. We also use this approximate time reversal to do rare event simulation.
Here we study large deviations in networks that are more likely to result from the accumulation of many slightly unusual events. We are particularly interested in analyzing large deviations where the most probable path changes direction. These deviations arise when a large deviation in one part of the system cascades across the network to produce a large deviation in another part of the network. Our technique involves the construction of an approximate time reversal. We also use this approximate time reversal to do rare event simulation.
2012, 8(4): 895-908
doi: 10.3934/jimo.2012.8.895
+[Abstract](3021)
+[PDF](344.9KB)
Abstract:
In this paper, we analyze an M/M/1 queueing system with working vacations and impatient customers. We examine the case that the customers' impatience is due to a working vacation. During a working vacation, customers are served at a slower than usual service rate and are likely to become impatient. Whenever a customer arrives in the system and realizes that the server is on vacation, the customer activates an ``impatience timer" which is exponentially distributed. If a customer's service has not been completed before the customer's timer expires, the customer leaves the queue, never to return. By analyzing this model, we derive the probability generating functions of the number of customers in the system when the server is in a service period and a working vacation, respectively. We further obtain the closed-form expressions for various performance measures, including the mean system size, the mean sojourn time of a customer served, the proportion of customers served and the rate of abandonment due to impatience. Finally, we present some numerical results to demonstrate effects of some parameters on these performance measures of the system.
In this paper, we analyze an M/M/1 queueing system with working vacations and impatient customers. We examine the case that the customers' impatience is due to a working vacation. During a working vacation, customers are served at a slower than usual service rate and are likely to become impatient. Whenever a customer arrives in the system and realizes that the server is on vacation, the customer activates an ``impatience timer" which is exponentially distributed. If a customer's service has not been completed before the customer's timer expires, the customer leaves the queue, never to return. By analyzing this model, we derive the probability generating functions of the number of customers in the system when the server is in a service period and a working vacation, respectively. We further obtain the closed-form expressions for various performance measures, including the mean system size, the mean sojourn time of a customer served, the proportion of customers served and the rate of abandonment due to impatience. Finally, we present some numerical results to demonstrate effects of some parameters on these performance measures of the system.
2012, 8(4): 909-924
doi: 10.3934/jimo.2012.8.909
+[Abstract](1958)
+[PDF](419.5KB)
Abstract:
This paper develops a discrete-time risk model with general claim sizes in a Markovian environment where both claim occurrence probabilities and the claim size distributions are dependent on the regime of the environment. We assume that the environmental regime is governed by a Markov process with a finite state space. We utilize a G/M/1 type structure in the process of the surplus level and the regime. We also employ the matrix analytic method to analyze the sojourn time of the surplus process at each level until the ruin time. Under this framework we obtain several important quantities related to ruin. First, we derive the penalty function using the results on the surplus process until the ruin time. Second, we obtain the ruin probability, the ruin time distribution and the deficit distribution at ruin. Numerical examples implement the ruin quantities that we derive.
This paper develops a discrete-time risk model with general claim sizes in a Markovian environment where both claim occurrence probabilities and the claim size distributions are dependent on the regime of the environment. We assume that the environmental regime is governed by a Markov process with a finite state space. We utilize a G/M/1 type structure in the process of the surplus level and the regime. We also employ the matrix analytic method to analyze the sojourn time of the surplus process at each level until the ruin time. Under this framework we obtain several important quantities related to ruin. First, we derive the penalty function using the results on the surplus process until the ruin time. Second, we obtain the ruin probability, the ruin time distribution and the deficit distribution at ruin. Numerical examples implement the ruin quantities that we derive.
2012, 8(4): 925-938
doi: 10.3934/jimo.2012.8.925
+[Abstract](1886)
+[PDF](383.6KB)
Abstract:
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive priority systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this decomposition property.
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive priority systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this decomposition property.
2012, 8(4): 939-968
doi: 10.3934/jimo.2012.8.939
+[Abstract](1960)
+[PDF](502.8KB)
Abstract:
In this paper we present the analysis of an M/M/c multiple synchronous vacation model. In contrast to the previous works on synchronous vacation model we consider the model with gated service discipline and with independent and identically distributed vacation periods. The analysis of this model requires different methodology compared to those ones used for synchronous vacation model so far. We provide the probability-generating function and the mean of the stationary number of customers at an arbitrary epoch as well as the Laplace-Stieljes transform and the mean of the stationary waiting time. The stationary distribution of the number of busy servers and the stability of the system are also considered. In the final part of the paper numerical examples illustrate the computational procedure.
This vacation queue is suitable to model a single operator controlled system consisting of more machines. Hence the provided analysis can be applied to study and optimize such systems.
In this paper we present the analysis of an M/M/c multiple synchronous vacation model. In contrast to the previous works on synchronous vacation model we consider the model with gated service discipline and with independent and identically distributed vacation periods. The analysis of this model requires different methodology compared to those ones used for synchronous vacation model so far. We provide the probability-generating function and the mean of the stationary number of customers at an arbitrary epoch as well as the Laplace-Stieljes transform and the mean of the stationary waiting time. The stationary distribution of the number of busy servers and the stability of the system are also considered. In the final part of the paper numerical examples illustrate the computational procedure.
This vacation queue is suitable to model a single operator controlled system consisting of more machines. Hence the provided analysis can be applied to study and optimize such systems.
2012, 8(4): 969-986
doi: 10.3934/jimo.2012.8.969
+[Abstract](1735)
+[PDF](1205.5KB)
Abstract:
The checkpoint and rollback scheme is a useful fault-tolerance method for mobile devices in wireless environments. Since battery power is one of the most critical resources for mobile devices, it is important to identify optimal checkpoint intervals that minimize power consumption. In this paper, we propose a method that minimizes power consumption in wireless remote checkpoint environments by considering environmental parameters such as device failure rate, wireless link error rate, and checkpoint overhead. To evaluate the proposed solution, we conducted analytical estimations, simulations, and experimental measurements in a real test-bed.
The checkpoint and rollback scheme is a useful fault-tolerance method for mobile devices in wireless environments. Since battery power is one of the most critical resources for mobile devices, it is important to identify optimal checkpoint intervals that minimize power consumption. In this paper, we propose a method that minimizes power consumption in wireless remote checkpoint environments by considering environmental parameters such as device failure rate, wireless link error rate, and checkpoint overhead. To evaluate the proposed solution, we conducted analytical estimations, simulations, and experimental measurements in a real test-bed.
2012, 8(4): 987-1015
doi: 10.3934/jimo.2012.8.987
+[Abstract](1947)
+[PDF](868.5KB)
Abstract:
This study analyzed a logistics system consisting of a supplier that produces and delivers a single product and a buyer that receives and sells the product to retail customers. In this type of logistics system, the supplier and the buyer agree upon a contract specifying that the supplier will deliver the amount of product needed to increase the inventory of the buyer up to a predetermined order-up-to level at the beginning of each time period. A mathematical model was developed to construct methods to find the cost minimizing cycle lengths for both parties and the order-up-to level for the buyer. The proposed methods were tested for accuracy and execution speed in a variety of experimental settings. Analysis of the results revealed that the proposed methods determined the optimal control parameters for each party in a short time frame. Ultimately, a coordination mechanism based on a system-wide cost minimization policy was proposed to ensure that system-wide costs are minimized while, at the same time, both parties benefit from coordinating their efforts.
This study analyzed a logistics system consisting of a supplier that produces and delivers a single product and a buyer that receives and sells the product to retail customers. In this type of logistics system, the supplier and the buyer agree upon a contract specifying that the supplier will deliver the amount of product needed to increase the inventory of the buyer up to a predetermined order-up-to level at the beginning of each time period. A mathematical model was developed to construct methods to find the cost minimizing cycle lengths for both parties and the order-up-to level for the buyer. The proposed methods were tested for accuracy and execution speed in a variety of experimental settings. Analysis of the results revealed that the proposed methods determined the optimal control parameters for each party in a short time frame. Ultimately, a coordination mechanism based on a system-wide cost minimization policy was proposed to ensure that system-wide costs are minimized while, at the same time, both parties benefit from coordinating their efforts.
2012, 8(4): 1017-1038
doi: 10.3934/jimo.2012.8.1017
+[Abstract](2265)
+[PDF](496.1KB)
Abstract:
Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading effects the objective function becomes nondifferentiable and has many local minima in the solution space. Traditional methods may fail to reach the global solution of ED problems. Most of the existing stochastic methods try to make the solution feasible or penalize an infeasible solution with penalty function method. However, to find the appropriate penalty parameter is not an easy task. Differential evolution is a population-based heuristic approach that has been shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution based solution technique along with a tournament selection that makes pair-wise comparison among feasible and infeasible solutions based on the degree of constraint violation for economic dispatch problems. We reformulate the nonsmooth objective function to a smooth one and add nonlinear inequality constraints to original ED problems. We consider five ED problems and compare the obtained results with existing standard deterministic NLP solvers as well as with other stochastic techniques available in literature.
Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading effects the objective function becomes nondifferentiable and has many local minima in the solution space. Traditional methods may fail to reach the global solution of ED problems. Most of the existing stochastic methods try to make the solution feasible or penalize an infeasible solution with penalty function method. However, to find the appropriate penalty parameter is not an easy task. Differential evolution is a population-based heuristic approach that has been shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution based solution technique along with a tournament selection that makes pair-wise comparison among feasible and infeasible solutions based on the degree of constraint violation for economic dispatch problems. We reformulate the nonsmooth objective function to a smooth one and add nonlinear inequality constraints to original ED problems. We consider five ED problems and compare the obtained results with existing standard deterministic NLP solvers as well as with other stochastic techniques available in literature.
2012, 8(4): 1039-1056
doi: 10.3934/jimo.2012.8.1039
+[Abstract](2474)
+[PDF](1419.2KB)
Abstract:
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.
2012, 8(4): 1057-1069
doi: 10.3934/jimo.2012.8.1057
+[Abstract](2963)
+[PDF](566.7KB)
Abstract:
The joint feature selection problem arises in many fields including computer vision, text classification and biomedical informatics. Generally, recent results show that it can be realized by solving a $\ell_{2,1}$-norm involved minimization problem. However, solving the optimization problem is a challenging task due to the non-smoothness of the regularization term. In this paper, we reformulate the problem to an equivalent constrained minimization problem by introducing an auxiliary variable. We split the corresponding augmented Lagrange function and minimize the subproblem alternatively with one variable by fixing the other one. Moreover, we linearize the subproblem and add a proximal-point term when the closed-form solutions are not easily to derived. The convergence analysis and the relatedness with other algorithms are also given. Although the $\ell_{2,1}$-norm is mainly considered, we show that the $\ell_{\infty,1}$-norm penalized learning problem can also be readily solved in our framework. The reported experiments on simulated and real data sets show that the proposed method is effective and promising. The performance comparisons illustrate that the proposed algorithm is competitive with even performs little better than the state-of-the-art solver SLEP.
The joint feature selection problem arises in many fields including computer vision, text classification and biomedical informatics. Generally, recent results show that it can be realized by solving a $\ell_{2,1}$-norm involved minimization problem. However, solving the optimization problem is a challenging task due to the non-smoothness of the regularization term. In this paper, we reformulate the problem to an equivalent constrained minimization problem by introducing an auxiliary variable. We split the corresponding augmented Lagrange function and minimize the subproblem alternatively with one variable by fixing the other one. Moreover, we linearize the subproblem and add a proximal-point term when the closed-form solutions are not easily to derived. The convergence analysis and the relatedness with other algorithms are also given. Although the $\ell_{2,1}$-norm is mainly considered, we show that the $\ell_{\infty,1}$-norm penalized learning problem can also be readily solved in our framework. The reported experiments on simulated and real data sets show that the proposed method is effective and promising. The performance comparisons illustrate that the proposed algorithm is competitive with even performs little better than the state-of-the-art solver SLEP.
2019 Impact Factor: 1.366
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