Minimax Theory and its Applications 09 (2024), No. 2, 341--356
Copyright Heldermann Verlag 2024
On Efficient Solutions for Semidefinite Linear Fractional Vector Optimization Problems
Moon Hee Kim
College of General Education, Tongmyong University, Busan 48520, Korea
mooni@tu.ac.kr
Gue Myung Lee
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
gmlee@pknu.ac.kr
We consider a semidefinite linear fractional vector optimization problem (FVP) and establish optimality theorem for efficient solutions for (FVP), which hold without any constraint qualification and which are expressed by sequences. Moreover, we discuss the relations between properly efficient solution of (FVP) and one of its related linear vector optimization problem (LVP). By using the relation, we obtain optimality theorem for properly efficient solutions for (FVP), which hold without any constraint qualification and which are expressed by sequences. Also, by using optimality theorem for efficient solutions of (FVP) and the relations, we obtain the semi-definite version of the Isermann's result for (FVP), which gives a sufficient condition that an efficient solution of (FVP) can be properly efficient for (FVP). We give examples for our results for properly efficient solutions for (FVP). Moreover, we formulate vector dual problem (VD) for (FVP) and establish duality theorems for (FVP) and (VD). Our approach for getting our main resuts is to use linear vector optimization problems related to (FVP).
Keywords: Semidefinite linear fractional vector optimization problem, efficient solutions, properly efficient solutions, optimality conditions, vector dual problem, weak duality theorem, strong duality theorem.
MSC: 90C25, 90C30, 90C46.
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