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1547-5816
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1553-166X
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Journal of Industrial & Management Optimization
October 2005 , Volume 1 , Issue 4
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2005, 1(4): 415-432
doi: 10.3934/jimo.2005.1.415
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Abstract:
In Operations Research, the equipment replacement process is usually modeled as a discrete sequential decision problem. The alternative approach is developed in vintage capital models, which explicitly involve the lifetime of capital equipment and are described by the integral equations of a special type. The paper exposes a general investigation framework for the optimal control of the integral models with endogenous lags, which is applied to meaningful one- and two-sector vintage models. The analysis leads to nontrivial results such as turnpike properties of the optimal equipment lifetime and corresponding management strategies of equipment replacement.
In Operations Research, the equipment replacement process is usually modeled as a discrete sequential decision problem. The alternative approach is developed in vintage capital models, which explicitly involve the lifetime of capital equipment and are described by the integral equations of a special type. The paper exposes a general investigation framework for the optimal control of the integral models with endogenous lags, which is applied to meaningful one- and two-sector vintage models. The analysis leads to nontrivial results such as turnpike properties of the optimal equipment lifetime and corresponding management strategies of equipment replacement.
2005, 1(4): 433-442
doi: 10.3934/jimo.2005.1.433
+[Abstract](1815)
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This paper presents the result of extensive computational experiments on an internationally diversified investment model using a large number of individual stocks and bonds in a single stock-bond integrated mean risk framework. This model was proposed by one of the authors in 1997 and was shown to perform better than standard asset allocation strategy when the universe is the set of stocks and bonds of Japan and U.S. In this paper, we extend the universe to over 3500 assets consisting of stocks of 46 countries and bonds of 20 countries and compare the integrated approach with other well used methods. Computational experiments show that the integrated approach is superior to the traditional methods.
This paper presents the result of extensive computational experiments on an internationally diversified investment model using a large number of individual stocks and bonds in a single stock-bond integrated mean risk framework. This model was proposed by one of the authors in 1997 and was shown to perform better than standard asset allocation strategy when the universe is the set of stocks and bonds of Japan and U.S. In this paper, we extend the universe to over 3500 assets consisting of stocks of 46 countries and bonds of 20 countries and compare the integrated approach with other well used methods. Computational experiments show that the integrated approach is superior to the traditional methods.
2005, 1(4): 443-463
doi: 10.3934/jimo.2005.1.443
+[Abstract](1791)
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Abstract:
We study the problem of optimal staged purchases of electricity in time-sequential deregulated electricity markets. In recent years, the electricity industry has been deregulated and multiple time-sequential auction markets, such as the block forward, the day-ahead and the hour-of, and the real-time electricity markets, are formed. Thus, a load serving entity need to purchase electricity in these markets economically to meet its demand in each settlement time interval. We use the stochastic dynamic programming approach to establish a condition for staged purchases of electricity to be optimal and study its properties. Two algorithms for computing the optimal staged purchases are also developed.
We study the problem of optimal staged purchases of electricity in time-sequential deregulated electricity markets. In recent years, the electricity industry has been deregulated and multiple time-sequential auction markets, such as the block forward, the day-ahead and the hour-of, and the real-time electricity markets, are formed. Thus, a load serving entity need to purchase electricity in these markets economically to meet its demand in each settlement time interval. We use the stochastic dynamic programming approach to establish a condition for staged purchases of electricity to be optimal and study its properties. Two algorithms for computing the optimal staged purchases are also developed.
2005, 1(4): 465-476
doi: 10.3934/jimo.2005.1.465
+[Abstract](2373)
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Abstract:
The purpose of the paper is to apply a nonlinear programming algorithm for computing kernel and related parameters of a support vector machine (SVM) by a two-level approach. Available training data are split into two groups, one set for formulating a quadratic SVM with $L_2$-soft margin and another one for minimizing the generalization error, where the optimal SVM variables are inserted. Subsequently, the total generalization error is evaluated for a separate set of test data. Derivatives of functions by which the optimization problem is defined, are evaluated in an analytical way, where an existing Cholesky decomposition needed for solving the quadratic SVM, is exploited. The approach is implemented and tested on a couple of standard data sets with up to 4,800 patterns. The results show a significant reduction of the generalization error, an increase of the margin, and a reduction of the number of support vectors in all cases where the data sets are sufficiently large. By a second set of test runs, kernel parameters are assigned to individual features. Redundant attributes are identified and suitable relative weighting factors are computed.
The purpose of the paper is to apply a nonlinear programming algorithm for computing kernel and related parameters of a support vector machine (SVM) by a two-level approach. Available training data are split into two groups, one set for formulating a quadratic SVM with $L_2$-soft margin and another one for minimizing the generalization error, where the optimal SVM variables are inserted. Subsequently, the total generalization error is evaluated for a separate set of test data. Derivatives of functions by which the optimization problem is defined, are evaluated in an analytical way, where an existing Cholesky decomposition needed for solving the quadratic SVM, is exploited. The approach is implemented and tested on a couple of standard data sets with up to 4,800 patterns. The results show a significant reduction of the generalization error, an increase of the margin, and a reduction of the number of support vectors in all cases where the data sets are sufficiently large. By a second set of test runs, kernel parameters are assigned to individual features. Redundant attributes are identified and suitable relative weighting factors are computed.
2005, 1(4): 477-486
doi: 10.3934/jimo.2005.1.477
+[Abstract](2751)
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Abstract:
Linear fractional vector optimization (LFVO) problems form a special class of nonconvex multiobjective optimization problems which has a significant role both in the management science and in the theory of vector optimization. Up to now, only LFVO problems with at most two connected components in the solution sets have been discussed in the literature. We propose some examples of LFVO problems with three or more connected components in the solution sets. It is proved that for any integer $m$ there exist LFVO problems with $m$ objective criteria whose solution sets have exactly $m$ connected components. Besides, we have solved the conjecture saying that $\chi(E(\mbox{P}))\leq \min\{m,\mbox{dim}0^+D+1\},$ where $\chi(E(\mbox{P}))$ is the number of connected components in the efficient solution set of a LFVO problem $(\mbox{P})$, $m$ is the number of the objective criteria of $(\mbox{P})$, and $\mbox{dim}0^+D$ is the dimension of the recession cone $0^+D$ of the feasible domain $D$ of $(\mbox{P})$. These new facts are useful for analyzing the practical problems which can be modeled as quasiconcave vector maximization problems in general, and as LFVO problems on unbounded feasible domains in particular.
Linear fractional vector optimization (LFVO) problems form a special class of nonconvex multiobjective optimization problems which has a significant role both in the management science and in the theory of vector optimization. Up to now, only LFVO problems with at most two connected components in the solution sets have been discussed in the literature. We propose some examples of LFVO problems with three or more connected components in the solution sets. It is proved that for any integer $m$ there exist LFVO problems with $m$ objective criteria whose solution sets have exactly $m$ connected components. Besides, we have solved the conjecture saying that $\chi(E(\mbox{P}))\leq \min\{m,\mbox{dim}0^+D+1\},$ where $\chi(E(\mbox{P}))$ is the number of connected components in the efficient solution set of a LFVO problem $(\mbox{P})$, $m$ is the number of the objective criteria of $(\mbox{P})$, and $\mbox{dim}0^+D$ is the dimension of the recession cone $0^+D$ of the feasible domain $D$ of $(\mbox{P})$. These new facts are useful for analyzing the practical problems which can be modeled as quasiconcave vector maximization problems in general, and as LFVO problems on unbounded feasible domains in particular.
2005, 1(4): 487-497
doi: 10.3934/jimo.2005.1.487
+[Abstract](2255)
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Abstract:
A fixed point iterative scheme is used for the simultaneous recovery of Lamé parameters in linear elasticity. Auxiliary problems principle applied to an output least-squares based regularized minimization problem results in a strongly convergent iterative scheme. When the (coefficient-dependent) energy norm is used, the condition ensuring the strong convergence are much milder and avoid any possibility of over-regularization.
A fixed point iterative scheme is used for the simultaneous recovery of Lamé parameters in linear elasticity. Auxiliary problems principle applied to an output least-squares based regularized minimization problem results in a strongly convergent iterative scheme. When the (coefficient-dependent) energy norm is used, the condition ensuring the strong convergence are much milder and avoid any possibility of over-regularization.
2005, 1(4): 499-512
doi: 10.3934/jimo.2005.1.499
+[Abstract](2390)
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Abstract:
In this paper we consider the question of sensor scheduling in discrete time. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to select one source (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem. By analyzing the positive semi-definite property of the error covariance matrix, we develop a branch and bound method to calculate the optimal scheduling strategy and give a numerical result for interpretation.
In this paper we consider the question of sensor scheduling in discrete time. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to select one source (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem. By analyzing the positive semi-definite property of the error covariance matrix, we develop a branch and bound method to calculate the optimal scheduling strategy and give a numerical result for interpretation.
2005, 1(4): 513-531
doi: 10.3934/jimo.2005.1.513
+[Abstract](2285)
+[PDF](241.1KB)
Abstract:
We study a single-period two-stage service-constrained supply chain with an information update. The buyer has two purchasing instances: before and after the forecast update. The procurement cost at the second stage is uncertain at the first stage. We determine the optimal ordering policy with two service constraints (a service constraint is imposed for each procurement stage) and discuss the impact of the forecast quality. Finally, we extend our model to a multi-period problem with two ordering stages in each period.
We study a single-period two-stage service-constrained supply chain with an information update. The buyer has two purchasing instances: before and after the forecast update. The procurement cost at the second stage is uncertain at the first stage. We determine the optimal ordering policy with two service constraints (a service constraint is imposed for each procurement stage) and discuss the impact of the forecast quality. Finally, we extend our model to a multi-period problem with two ordering stages in each period.
2005, 1(4): 533-547
doi: 10.3934/jimo.2005.1.533
+[Abstract](2791)
+[PDF](230.1KB)
Abstract:
In this paper, a new quadratic smoothing approximation to the $l_1$ exact penalty function is proposed. It is shown that under certain conditions, if there exists a global minimizer of the original constrained optimization problem in the ''interior'' of the feasible set of the original constrained optimization problem, then any global minimizer of the smoothed penalty problem is a global minimizer of the original constrained optimization problem when the penalty parameter is sufficiently large; and if the feasible region of the original constrained optimization problem is ''robust'', then any global minimizer of the smoothed penalty problem is a feasible approximate global minimizer of the original constrained optimization problem when the penalty parameter is sufficiently large, and the precision of the approximation can be set in advance. Some numerical examples are given to illustrate that constrained optimization problems can be well solved by the present smoothing scheme.
In this paper, a new quadratic smoothing approximation to the $l_1$ exact penalty function is proposed. It is shown that under certain conditions, if there exists a global minimizer of the original constrained optimization problem in the ''interior'' of the feasible set of the original constrained optimization problem, then any global minimizer of the smoothed penalty problem is a global minimizer of the original constrained optimization problem when the penalty parameter is sufficiently large; and if the feasible region of the original constrained optimization problem is ''robust'', then any global minimizer of the smoothed penalty problem is a feasible approximate global minimizer of the original constrained optimization problem when the penalty parameter is sufficiently large, and the precision of the approximation can be set in advance. Some numerical examples are given to illustrate that constrained optimization problems can be well solved by the present smoothing scheme.
2005, 1(4): 549-563
doi: 10.3934/jimo.2005.1.549
+[Abstract](1997)
+[PDF](275.8KB)
Abstract:
In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility ''to doubl'' the number of concepts when a constrained problem is considered. In particular we introduce sense I and sense II isolated minimizers, properly efficient points, efficient points and weakly efficient points. As a motivation leading to these concepts we give some results concerning optimality conditions in constrained vector optimization and stability properties of isolated minimizers and properly efficient points. Our main investigation and results concern relations between sense I and sense II concepts. These relations are proved often under convexity type conditions.
In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility ''to doubl'' the number of concepts when a constrained problem is considered. In particular we introduce sense I and sense II isolated minimizers, properly efficient points, efficient points and weakly efficient points. As a motivation leading to these concepts we give some results concerning optimality conditions in constrained vector optimization and stability properties of isolated minimizers and properly efficient points. Our main investigation and results concern relations between sense I and sense II concepts. These relations are proved often under convexity type conditions.
2005, 1(4): 565-587
doi: 10.3934/jimo.2005.1.565
+[Abstract](2086)
+[PDF](685.2KB)
Abstract:
We consider the task of estimating the relative pose (position and orientation) between a 3D object and its projection on a 2D image plane from a set of point correspondences. Our approach is to formulate the task as an unconstrained optimization problem on the intersection of the special orthogonal group and a cone, and exploit as much as possible the geometry of the underlying parameter space. The optimization does not require Riemannian geometry. It involves successive parameterization of the constraint manifold and is based on Newton-type iterations in local parameter space. A direct proof of local quadratical convergence to the optimum is provided. A key feature of the proposed approach, not used in earlier studies, is an analytic geodesic search, alternating between gradient, Gauss, Newton and random directions, which ensures the escape from local minima and convergence to a global minimum without the need to reinitialize the algorithm. Indeed, for a prescribed number of iterations, the proposed algorithm achieves significantly lower pose estimation errors than earlier methods and it converges to a global minimum in typically 5--10 iterations.
We consider the task of estimating the relative pose (position and orientation) between a 3D object and its projection on a 2D image plane from a set of point correspondences. Our approach is to formulate the task as an unconstrained optimization problem on the intersection of the special orthogonal group and a cone, and exploit as much as possible the geometry of the underlying parameter space. The optimization does not require Riemannian geometry. It involves successive parameterization of the constraint manifold and is based on Newton-type iterations in local parameter space. A direct proof of local quadratical convergence to the optimum is provided. A key feature of the proposed approach, not used in earlier studies, is an analytic geodesic search, alternating between gradient, Gauss, Newton and random directions, which ensures the escape from local minima and convergence to a global minimum without the need to reinitialize the algorithm. Indeed, for a prescribed number of iterations, the proposed algorithm achieves significantly lower pose estimation errors than earlier methods and it converges to a global minimum in typically 5--10 iterations.
2005, 1(4): 588-588
doi: 10.3934/jimo.2005.1.588
+[Abstract](1811)
+[PDF](25.8KB)
Abstract:
In Volume 1, 2005, issue number 3 on pages 275-287 of Journal of Industrial and Management Optimization (JIMO), we published an article by J. Wu et al. entitled ''Supply contract model with service level constraint.''The article went through our usual rigorous refereeing process and it was recommended by referees and the guest editors for publication. Recently, Dr. Wu has written to Professor S. Sethi and to the Editor-in-Chief, Professor K.L. Teo, apologizing for not indicating that the mathematical model, analyses and results of their article were primarily from the following working paper: '' S. Sethi, H. Yan and H. Zhang, ''Information Updated Supply Chain with Service-level Constraints'', Working Paper, School of Management, University of Texas at Dallas, 2003.
In Volume 1, 2005, issue number 3 on pages 275-287 of Journal of Industrial and Management Optimization (JIMO), we published an article by J. Wu et al. entitled ''Supply contract model with service level constraint.''The article went through our usual rigorous refereeing process and it was recommended by referees and the guest editors for publication. Recently, Dr. Wu has written to Professor S. Sethi and to the Editor-in-Chief, Professor K.L. Teo, apologizing for not indicating that the mathematical model, analyses and results of their article were primarily from the following working paper: '' S. Sethi, H. Yan and H. Zhang, ''Information Updated Supply Chain with Service-level Constraints'', Working Paper, School of Management, University of Texas at Dallas, 2003.
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