ISSN:
1547-5816
eISSN:
1553-166X
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Journal of Industrial & Management Optimization
January 2005 , Volume 1 , Issue 1
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2005, 1(1): i-i
doi: 10.3934/jimo.2005.1.1i
+[Abstract](1062)
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Abstract:
It is with great pleasure that we bring to you the inaugural issue of the Journal of Industrial and Management Optimization (JIMO), published by the American Institute of Mathematical Sciences.
It is with great pleasure that we bring to you the inaugural issue of the Journal of Industrial and Management Optimization (JIMO), published by the American Institute of Mathematical Sciences.
2005, 1(1): iii-iii
doi: 10.3934/jimo.2005.1.1iii
+[Abstract](975)
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Abstract:
This inaugural issue of JIMO is dedicated to Professor Franco Giannessi on the occasion of his 70th birthday and in recognition of his many fundamental contributions in optimization and optimal control. During his long career, through his tremendous work Professor Giannessi has influenced many researchers on their scientific activity of in the areas of optimization and optimal control. Professor Franco Giannessi has won the admiration and affection of those who know him. It fits that this special issue is dedicated to him because not only he has been a major contributor in the field but also he has long association with many members of the Editorial Board of JIMO and he always offers his support and encouragement in their career and scientific development. Professor Franco Giannessi is an outstanding scholar, and excellent colleague and friend.
For the full preface, please click the "Full Text" button above.
This inaugural issue of JIMO is dedicated to Professor Franco Giannessi on the occasion of his 70th birthday and in recognition of his many fundamental contributions in optimization and optimal control. During his long career, through his tremendous work Professor Giannessi has influenced many researchers on their scientific activity of in the areas of optimization and optimal control. Professor Franco Giannessi has won the admiration and affection of those who know him. It fits that this special issue is dedicated to him because not only he has been a major contributor in the field but also he has long association with many members of the Editorial Board of JIMO and he always offers his support and encouragement in their career and scientific development. Professor Franco Giannessi is an outstanding scholar, and excellent colleague and friend.
For the full preface, please click the "Full Text" button above.
2005, 1(1): 1-19
doi: 10.3934/jimo.2005.1.1
+[Abstract](1717)
+[PDF](255.4KB)
Abstract:
Firms that want to increase the sales of their brands through advertising have the choice of capturing market share from their competitors through brand advertising, or increasing primary demand for the category through generic advertising. In this paper, differential game theory is used to analyze the effects of the two types of advertising decisions made by firms offering a product in a dynamic duopoly. Each firm's sales depend not only on its own and its competitor's brand advertising strategies, but also on the generic advertising expenditures of the two firms. Closed-loop Nash equilibrium solutions are obtained for symmetric and asymmetric competitors in a finite-horizon setting. The analysis for the symmetric case results in explicit solutions, and numerical techniques are employed to solve the problem for asymmetric firms.
Firms that want to increase the sales of their brands through advertising have the choice of capturing market share from their competitors through brand advertising, or increasing primary demand for the category through generic advertising. In this paper, differential game theory is used to analyze the effects of the two types of advertising decisions made by firms offering a product in a dynamic duopoly. Each firm's sales depend not only on its own and its competitor's brand advertising strategies, but also on the generic advertising expenditures of the two firms. Closed-loop Nash equilibrium solutions are obtained for symmetric and asymmetric competitors in a finite-horizon setting. The analysis for the symmetric case results in explicit solutions, and numerical techniques are employed to solve the problem for asymmetric firms.
2005, 1(1): 21-32
doi: 10.3934/jimo.2005.1.21
+[Abstract](1113)
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Abstract:
The paper aims to analyse and compare two different approaches to optimality conditions for multiobjective optimization problems, which involve nonsmooth functions. Both necessary and sufficient first order conditions are presented for the case in which constraint is given just as a set. Finally, the optimality conditions based on these two approaches are compared.
The paper aims to analyse and compare two different approaches to optimality conditions for multiobjective optimization problems, which involve nonsmooth functions. Both necessary and sufficient first order conditions are presented for the case in which constraint is given just as a set. Finally, the optimality conditions based on these two approaches are compared.
2005, 1(1): 33-38
doi: 10.3934/jimo.2005.1.33
+[Abstract](1148)
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Abstract:
Given a generic dual program we discuss the absence of duality gap for a family of Lagrange-type functions. We obtain necessary conditions that become sufficient ones under some additional assumptions. We also give examples of Lagrange-type functions for which this sufficient conditions hold.
Given a generic dual program we discuss the absence of duality gap for a family of Lagrange-type functions. We obtain necessary conditions that become sufficient ones under some additional assumptions. We also give examples of Lagrange-type functions for which this sufficient conditions hold.
2005, 1(1): 39-52
doi: 10.3934/jimo.2005.1.39
+[Abstract](1141)
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Abstract:
An evolutionary model is presented for a multi-sector, multi-instrument financial equilibrium problem, with general utility function and including policy interventions in the form of taxes and price controls. We give the evolutionary financial equilibrium condition, prove an equivalent variational inequality formulation, from which an existence result follows.
An evolutionary model is presented for a multi-sector, multi-instrument financial equilibrium problem, with general utility function and including policy interventions in the form of taxes and price controls. We give the evolutionary financial equilibrium condition, prove an equivalent variational inequality formulation, from which an existence result follows.
2005, 1(1): 53-63
doi: 10.3934/jimo.2005.1.53
+[Abstract](1207)
+[PDF](244.4KB)
Abstract:
This paper presents a duality theory for solving concave minimization problem and nonconvex quadratic programming problem subjected to nonlinear inequality constraints. By use of the canonical dual transformation developed recently, two canonical dual problems are formulated, respectively. These two dual problems are perfectly dual to the primal problems with zero duality gap. It is proved that the sufficient conditions for global minimizers and local extrema (both minima and maxima) are controlled by the triality theory discovered recently [5]. This triality theory can be used to develop certain useful primal-dual methods for solving difficult nonconvex minimization problems. Results shown that the difficult quadratic minimization problem with quadratic constraint can be converted into a one-dimensional dual problem, which can be solved completely to obtain all KKT points and global minimizer.
This paper presents a duality theory for solving concave minimization problem and nonconvex quadratic programming problem subjected to nonlinear inequality constraints. By use of the canonical dual transformation developed recently, two canonical dual problems are formulated, respectively. These two dual problems are perfectly dual to the primal problems with zero duality gap. It is proved that the sufficient conditions for global minimizers and local extrema (both minima and maxima) are controlled by the triality theory discovered recently [5]. This triality theory can be used to develop certain useful primal-dual methods for solving difficult nonconvex minimization problems. Results shown that the difficult quadratic minimization problem with quadratic constraint can be converted into a one-dimensional dual problem, which can be solved completely to obtain all KKT points and global minimizer.
2005, 1(1): 65-80
doi: 10.3934/jimo.2005.1.65
+[Abstract](1226)
+[PDF](220.3KB)
Abstract:
Supervisory control belongs essentially to the logic level for control problems in discrete event systems (DESs) and its corresponding control task is hard. This is unlike many practical optimal control problems which belong to the performance level and whose control tasks are soft. In this paper, we present two new optimal control problems of DESs: one with cost functions for choosing control inputs, and the other for occurring events. Their performance measures are to minimize the maximal discounted total cost among all possible strings that the system generates. Since this is a nonlinear optimization problem, we model such systems by using Markov decision processes. We then present the optimality equations for both control problems and obtain their optimal solutions. When the cost functions are stationary, we show that both the optimality equations and their solutions are also stationary. We then use these equations and solutions to describe and solve uniformly the basic synthesizing problems in the two branches of the supervisory control area: those being the event feedback control and the state feedback control. Moreover, we show that the control invariant languages and the control invariant predicates with their permissive supervisors and state feedbacks not only have meanings in supervisory control of DESs, but are also the optimal solutions for some optimal control problems. This shows a link existing between the logic level and the performance level for the control of discrete event systems. Finally, a numerical example is given to illustrate some results for supervisory control of a DES.
Supervisory control belongs essentially to the logic level for control problems in discrete event systems (DESs) and its corresponding control task is hard. This is unlike many practical optimal control problems which belong to the performance level and whose control tasks are soft. In this paper, we present two new optimal control problems of DESs: one with cost functions for choosing control inputs, and the other for occurring events. Their performance measures are to minimize the maximal discounted total cost among all possible strings that the system generates. Since this is a nonlinear optimization problem, we model such systems by using Markov decision processes. We then present the optimality equations for both control problems and obtain their optimal solutions. When the cost functions are stationary, we show that both the optimality equations and their solutions are also stationary. We then use these equations and solutions to describe and solve uniformly the basic synthesizing problems in the two branches of the supervisory control area: those being the event feedback control and the state feedback control. Moreover, we show that the control invariant languages and the control invariant predicates with their permissive supervisors and state feedbacks not only have meanings in supervisory control of DESs, but are also the optimal solutions for some optimal control problems. This shows a link existing between the logic level and the performance level for the control of discrete event systems. Finally, a numerical example is given to illustrate some results for supervisory control of a DES.
2005, 1(1): 81-86
doi: 10.3934/jimo.2005.1.81
+[Abstract](1301)
+[PDF](182.5KB)
Abstract:
A continuum model of transportation network with elastic demand is presented. The equilibrium conditions are expressed in terms of a Variational Inequality and some existence theorems are proved.
A continuum model of transportation network with elastic demand is presented. The equilibrium conditions are expressed in terms of a Variational Inequality and some existence theorems are proved.
2005, 1(1): 87-98
doi: 10.3934/jimo.2005.1.87
+[Abstract](1581)
+[PDF](250.5KB)
Abstract:
We will propose a new scheme to construct an index-plus-alpha portfolio which outperforms a given index by a small positive amount alpha. Among such methods is index tilting where the weight of an index tracking portfolio is slightly modified by taking into account the various information about individual assets. However, portfolios generated by these methods need not outperform the index, particularly when we compare the performance on the net basis, i.e., return after subtracting the transaction cost.
The method to be proposed in this paper is to calculate a portfolio which keeps track of an index-plus-alpha portfolio with minimal transaction cost. The problem is formulated as a concave minimization under linear constraints, which can be solved in an efficient manner by a branch and bound algorithm. We will demonstrate that this method can usually outperform the given index when alpha is chosen in an appropriate manner.
We will propose a new scheme to construct an index-plus-alpha portfolio which outperforms a given index by a small positive amount alpha. Among such methods is index tilting where the weight of an index tracking portfolio is slightly modified by taking into account the various information about individual assets. However, portfolios generated by these methods need not outperform the index, particularly when we compare the performance on the net basis, i.e., return after subtracting the transaction cost.
The method to be proposed in this paper is to calculate a portfolio which keeps track of an index-plus-alpha portfolio with minimal transaction cost. The problem is formulated as a concave minimization under linear constraints, which can be solved in an efficient manner by a branch and bound algorithm. We will demonstrate that this method can usually outperform the given index when alpha is chosen in an appropriate manner.
2005, 1(1): 99-122
doi: 10.3934/jimo.2005.1.99
+[Abstract](1293)
+[PDF](249.6KB)
Abstract:
We consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs), in which all decisions are required to be made here-and-now, before a random event is observed. We show that this kind of SMPEC plays a very important role in practice. In order to develop effective algorithms, we first give some reformulations of the SMPEC and then, based on these reformulations, we propose a smoothed penalty approach for solving the problem. A comprehensive convergence theory is also included.
We consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs), in which all decisions are required to be made here-and-now, before a random event is observed. We show that this kind of SMPEC plays a very important role in practice. In order to develop effective algorithms, we first give some reformulations of the SMPEC and then, based on these reformulations, we propose a smoothed penalty approach for solving the problem. A comprehensive convergence theory is also included.
2005, 1(1): 123-132
doi: 10.3934/jimo.2005.1.123
+[Abstract](1169)
+[PDF](176.1KB)
Abstract:
The theory of Vector Variational Inequalities can be based on the image space analysis and theorems of the alternative or separation theorems. Exploiting the separation approach for suitable approximations of the image associated to a Vector Variational Inequality, Lagrangian-type necessary optimality conditions are obtained. Applications to vector optimization problems and to vector traffic equilibria are briefly outlined.
The theory of Vector Variational Inequalities can be based on the image space analysis and theorems of the alternative or separation theorems. Exploiting the separation approach for suitable approximations of the image associated to a Vector Variational Inequality, Lagrangian-type necessary optimality conditions are obtained. Applications to vector optimization problems and to vector traffic equilibria are briefly outlined.
2005, 1(1): 133-148
doi: 10.3934/jimo.2005.1.133
+[Abstract](1490)
+[PDF](390.1KB)
Abstract:
In airfoil design, one problem of great interest is to find the target airfoil profile to achieve a given target velocity distribution. It can be formulated as an optimal control problem, with the control being the airfoil profile and the governing equation being the full potential equation in the transonic regime. To discretize the problem, one approach is to employ the finite element method. In the discretized space, a direct relationship between the objective function and the unknown profile co-ordinates can be defined via the finite element basis functions. Moreover, it is advantageous to derive the gradient in the discretized space rather than the continuous space to avoid contamination by discretization errors. In this paper, this approach is studied. In particular, a new formulation is proposed. A novel decomposition of the discrete space for the potential function, the gradient is derived and an efficient algorithm using the quasi-Newton method is described. In generating and adjusting the mesh during iterations, the elliptic mesh generation technique is used.
In airfoil design, one problem of great interest is to find the target airfoil profile to achieve a given target velocity distribution. It can be formulated as an optimal control problem, with the control being the airfoil profile and the governing equation being the full potential equation in the transonic regime. To discretize the problem, one approach is to employ the finite element method. In the discretized space, a direct relationship between the objective function and the unknown profile co-ordinates can be defined via the finite element basis functions. Moreover, it is advantageous to derive the gradient in the discretized space rather than the continuous space to avoid contamination by discretization errors. In this paper, this approach is studied. In particular, a new formulation is proposed. A novel decomposition of the discrete space for the potential function, the gradient is derived and an efficient algorithm using the quasi-Newton method is described. In generating and adjusting the mesh during iterations, the elliptic mesh generation technique is used.
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