• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.597-602
• /
• 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
• /
• v.19 no.1_2
• /
• pp.371-384
• /
• 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
• /
• v.27 no.3_4
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.351-360
• /
• 2005

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is $\eta$-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1257-1261
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.411-423
• /
• 2012

A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.

• Journal of applied mathematics & informatics
• /
• v.30 no.1_2
• /
• pp.111-125
• /
• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.83-99
• /
• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• 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
• /
• v.5 no.2
• /
• 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.