Using a two-criteria two-person game as an example, the validity of the scalarization method applied for the parameterization of the set of game values and for estimating the players' payoffs is investigated. It i...
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Using a two-criteria two-person game as an example, the validity of the scalarization method applied for the parameterization of the set of game values and for estimating the players' payoffs is investigated. It is shown that the use of linear scalarization by the players gives the results different from those obtained using Germeyer's scalarization. Various formalizations of the concept of value of MC games are discussed.
Motivated by the scalarization method in vector optimization theory, we take a new approach to fixed point theory on cone metric spaces. By using our method we prove some fixed point theorems and several common fixed ...
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Motivated by the scalarization method in vector optimization theory, we take a new approach to fixed point theory on cone metric spaces. By using our method we prove some fixed point theorems and several common fixed point theorems on cone metric spaces in which the cone need not be normal. Our results improve and generalize many well-known results from the literature. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, we consider both unconstrained and constrained uncertain vector optimization problems involving free disposal sets, and study the qualitative properties of their robust Benson efficient solutions. First...
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In this paper, we consider both unconstrained and constrained uncertain vector optimization problems involving free disposal sets, and study the qualitative properties of their robust Benson efficient solutions. First, we discuss necessary and sufficient optimality conditions for the robust Benson efficient solutions of these problems using the linear scalarization method. Then, by utilizing this approach, we investigate the semicontinuity properties of the solution maps when the problem data is perturbed by parameters given in parameter spaces. Finally, we suggest concepts of approximate robust Benson efficient solutions and investigate Hausdorff well-posedness conditions for such problems with respect to these approximate solutions. Several examples are provided to illustrate the applicability and novelty of the results obtained in this study.
In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general form...
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In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the epsilon-constraint method, the Benson method, the hybrid method and the elastic epsilon-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between epsilon-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and epsilon-optimal solutions of the introduced scalarized problem are achieved. (C) 2013 Elsevier B.V. All rights reserved.
In this paper we investigate the existence of Pareto equilibria in vector-valued extensive form games. In particular we show that every vector-valued extensive form game with perfect information has at least one subga...
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In this paper we investigate the existence of Pareto equilibria in vector-valued extensive form games. In particular we show that every vector-valued extensive form game with perfect information has at least one subgame perfect Pareto equilibrium in pure strategies. If one tries to prove this and develop a vector-valued backward induction procedure in analogy to the real-valued one, one sees that different effects may occur which thus have to be taken into account: First, suppose the deciding player at a nonterminal node makes a choice such that the equilibrium payoff vector of the subgame he would enter is undominated under the equilibrium payoff vectors of the other subgames he might enter. Then this choice need not to lead to a Pareto equilibrium. Second, suppose at a nonterminal node a chance move may arise. The combination of the Pareto equilibria of the subgames to give a strategy combination of the entire game need not be a Pareto equilibrium of the entire game. Furthermore we introduce an approach and an algorithm which allows us to determine several and all subgame perfect Pareto equilibria, respectively.
scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce...
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scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems.
We consider a single-macrocell heterogeneous multiple-input multiple-output network, where the macrocell shares the same frequency band with the femto network. The interference power to the macro users from the femto ...
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We consider a single-macrocell heterogeneous multiple-input multiple-output network, where the macrocell shares the same frequency band with the femto network. The interference power to the macro users from the femto base stations is kept below a threshold to guarantee that the performance of the macro users does not degrade due to the femto network. We consider the problem of finding the set of all achievable power-rate tuples for this setting. We first formulate a two-dimensional vector optimization problem in which we consider maximizing the sum-rate and minimizing the sum-power, subject to maximum power and interference threshold constraints. The considered problem is NP-hard. We provide a method to solve the problem by using the relationship between the weighted sum-rate maximization and weighted-sum-mean-squared-error minimization problems. Furthermore, using the proposed algorithm, we evaluate the impact of imposing interference threshold constraints and the impact of co-channel deployment in heterogeneous networks. The proposed algorithm can be used to evaluate the performance of real heterogeneous networks via off-line numerical simulations.
In this paper, a new noncooperative multiobjective constrained game is presented as a generalization of a multiobjective constrained game in finite-dimensional space. By using new continuity and convexity, the existen...
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In this paper, a new noncooperative multiobjective constrained game is presented as a generalization of a multiobjective constrained game in finite-dimensional space. By using new continuity and convexity, the existence of a solution of this mulitobjective constrained game is obtained. (C) 2003 Elsevier Science Ltd. All rights reserved.
This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are...
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This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are interested in finding the relationships between epsilon-(weakly, properly) efficient points of an MOP and epsilon-optimal solutions of the related scalarized problem. For this purpose, the relationships between epsilon is an element of R >= and epsilon is an element of R->=(m), for a single objective and multi-objective problems, respectively, are analyzed. In fact, necessary and/or sufficient conditions for approximating (weakly, properly) efficient points of a general MOP via approximate solutions of the scalarized problems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper, a scalarization result of epsilon-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of epsilon-weak efficient and epsilon-effici...
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In this paper, a scalarization result of epsilon-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of epsilon-weak efficient and epsilon-efficient solutions sets for the VEPs are proved under some suitable conditions in real Hausdorff topological vector spaces. The main results presented in this paper improve and generalize some known results in the literature.
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