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

• 대한수학회지
• /
• 제43권2호
• /
• pp.241-258
• /
• 2006

This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.

• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.75-106
• /
• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Journal of applied mathematics & informatics
• /
• 제32권1_2호
• /
• pp.153-159
• /
• 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
• /
• 제6권1호
• /
• pp.67-80
• /
• 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
• /
• 제5권3호
• /
• pp.797-804
• /
• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.433-455
• /
• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.819-837
• /
• 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 applied mathematics & informatics
• /
• 제32권3_4호
• /
• pp.491-502
• /
• 2014

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.603-619
• /
• 2009

Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.