• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.539-551
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• 2005

In this paper, sufficient optimality conditions and duality results for nonsmooth vector optimization problems are given under near invexity and infineness assumptions. Also, weak vector saddle-point theorems are obtained under near invexity-infineness assumptions.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.11-19
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• 2000

We give a new coincidence theorem for multimaps on generalized convex spaces and apply it to deduce s-saddle point and saddle point theorems.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.719-730
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• 1997

From a minimax inequality related to admissible multimaps, we deduce generalized versions of lopsided saddle point theorems, fixed point theorems, existence of maximizable linear functionals, the Walras excess demand theorem, and the Gale-Nikaido-Debreu theorem.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.723-734
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• 2013

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.597-602
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• 2013

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

• 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.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.491-504
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• 2018

In this article, we consider a fourth order nonlinear difference system. By making use of the critical point theory, we obtain some new existence theorems of at least one periodic solution with minimal period. Our main approach used in this article is the variational technique and the Saddle Point Theorem.