• 대한수학회지
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• 제41권5호
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.371-384
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• 2005

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1381-1395
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• 2009

Mixed type second order dual to the non-differentiable problem containing support functions is formulated and duality theorems are proved under generalized second order convexity conditions. It is pointed out that the mixed type duality results already reported in the literature are the special cases of our results.

• 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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• 제26권5_6호
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• pp.819-837
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• 2008

A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

• 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.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1257-1261
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• 2008

In this paper, we consider of a convexifiable programming problem with bounds on variables. We obtain Mond-Weir type duality theorems for the convexifiable programming problems. Moreover, we give a numerical example to illustrate our duality.

• 대한수학회논문집
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• 제28권2호
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• 대한수학회지
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• 제48권1호
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• pp.13-21
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• 2011

In this paper, a pair of Wolfe type nondifferentiable sec-ond order symmetric minimax mixed integer dual problems is formu-lated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

• Structural Engineering and Mechanics
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• 제26권1호
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• pp.15-30
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• 2007

In the paper, one focuses on the problem of duality in non-linear programming, applied to the solution of no-tension problems by means of Limit Analysis (LA) theorems for Not Resisting Tension (NRT) models. In details, one demonstrates that, starting from the application of the duality theory to the non-linear program defined by the static theorem approach for a discrete NRT model, this procedure results in the definition of a dual problem that has a significant physical meaning: the formulation of the kinematic theorem.