• East Asian mathematical journal
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• 제27권5호
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• pp.539-543
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• 2011

In this paper, we consider an optimization problem which consists a nonconvex quadratic objective function and two nonconvex quadratic constraint functions. We formulate its dual problem with semidefinite constraints, and we establish weak and strong duality theorems which hold between these two problems. And we give an example to illustrate our duality results. It is worth while noticing that our weak and strong duality theorems hold without convexity assumptions.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.151-160
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• 2008

A pair of multiobjective fractional symmetric dual programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are proved under pseudoinvexity assumptions. A self duality theorem is also discussed.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.153-159
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• 2014

In this paper, we introduce a pair of higher-order symmetric dual models/problems. Weak, strong and converse duality theorems for this pair are established under the assumption of higher-order invexity. Moreover, self duality theorem is also discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• East Asian mathematical journal
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• 제5권2호
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• pp.209-213
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• 1989

The efficiency(Pareto optimum) is a type of solutions for multiobjective programs. We formulate duality relations for multiobjective nonlinear programs by using the concept of efficiency. The results are the weak and strong duality relations for a vector dual of the Wolfe type involving invex functions.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.227-235
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• 2004

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.475-488
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• 1998

Wolfe and Mond-Weir type duals for multiobjective con-trol problems are formulated. Under pseudo-invexity/quasi-invexity assumptions of the functions involved, weak and strong duality the-orems are proved to relate efficient solutions of the primal and dual problems.

• 대한수학회논문집
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• 제28권3호
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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.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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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.

• 충청수학회지
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• 제29권3호
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• pp.465-475
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• 2016

We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.