• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Korean Management Science Review
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• v.10 no.2
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• pp.11-26
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• 1993

This paper presents a new interactive procedure for multiple objective linear programming problem (MOLP). In practical multiple objective linear programming applications, there is usually no need for the decision maker to consider solutions which are not efficient. Therefore, the interactive procedure presented here searches only among efficient solutions and terminates with a solution that is guaranteed to be efficient. It also can converge to nonextreme efficient final solutions rather than being restricted to only extreme efficient points of the feasible set. The procedure does not require sophisticated judgements or inputs from the decision maker. One of the most attractive features of the procedure however, is that the method allows the DM to examine the efficient faces it finds. As iteration goes, the DM can explore a wide variety of efficient faces rather than efficient faces confined to only certain subregion of the feasible set of problem MOLP since the efficient faces that the procedure finds need not be adjacent. This helps the DM explore the nature of the efficient set of problem MOLP and also helps the DM have confidence with a final solution. For these reasons, I feel that the procedure offer significant promise in solving multiple objective linear programs rapidly and in a satisfying manner to the DM.

• Journal of the military operations research society of Korea
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• v.14 no.1
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• pp.33-41
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• 1988

In Multiple Objective Linear Programming (MOLP), it is well known that efficient solution and weight are correspondent to each other. The purpose of this paper is to study relationships between efficient face and the region of weight in MOLP. It is shown that the regions of weights corresponding to two efficient extreme points are also neighbor if two efficient extreme points are neighbor each other, and that the set of the efficient solutions corresponding to the common part of weight regions is efficient face. Using the above, we present a method to find the efficient solutions corresponding to a given weight and vice versa.

• Journal of the military operations research society of Korea
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• v.13 no.2
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• pp.33-41
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• 1987

In Multiple Objective Linear Programming (MOLP), it is well known that efficient solution and weight are correspondent to each other. The purpose of this paper is to study relationships between efficient face and the region of weight in MOLP. It is shown that the regions of weights corresponding to two efficient extreme points are also neighbor if two efficient extreme points are neighbor each other, and that the set of the efficient solutions corresponding to the common part of weight regions is efficient face. Using the above, we present a method to find the efficient solutions corresponding to a given weight and vice versa.

• East Asian mathematical journal
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• v.39 no.5
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• pp.505-514
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• 2023

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.119-128
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• 1994

There are three important regions im Multiple Objective Linear Programming (MOLP). One is the region of efficient solutions, another is the region of weight to be used for finding efficient solutions, the third is the region of efficient (nondominated) objective values. In this paper, first, we find the condition of extreme point in the region of efficient objective values. Second, we find that the sum of the dimension of the weight region and the dimension of efficient objective values region is constant. Using the above, it is shown that we find the shape and dimension of weight region corresponding to the given region or efficient objective values and vice versa.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.1-7
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• 1993

Vector optimization problems consist of two or more objective functions and constraints. Optimization entails obtaining efficient solutions. Geoffrion [3] introduced the definition of the properly efficient solution in order to eliminate efficient solutions causing unbounded trade-offs between objective functions. In 1974, Isermann [7] obtained a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with linear constraints and showed that every efficient solution is a properly efficient solution. Since then, many authors [1, 2, 4, 5, 6] have extended the Isermann's results. In particular, Gulati and Islam [4] derived a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with nonlinear constraints, under certain assumptions. In this paper, we consider the following nonlinear vector optimization problem (NVOP): (Fig.) where for each i, f$_{i}$ is a differentiable function from R$^{n}$ into R and g is a differentiable function from R$^{n}$ into R$^{m}$ .

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.837-847
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• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.