Shashi Kant Mishra

Nondifferentiable multiobjective programming under generalized d-univexity

Abstract In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d -invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush–Kuhn–Tucker sufficient optimality condition and establish Mond–Weir type and general Mond–Weir type duality results for the nondifferentiable multiobjective programming problem.

Second order symmetric duality in multiobjective programming involving generalized cone-invex functions

Abstract In this paper, cone-second order pseudo-invex and strongly cone-second order pseudo-invex functions are defined. A pair of Mond–Weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are established under aforesaid generalized invexity assumptions. A second self-duality theorem is also given by assuming the functions involved to be skew-symmetric.

Non-differentiable higher-order symmetric duality in mathematical programming with generalized invexity

A pair of non-differentiable higher-order symmetric dual model in mathematical programming is formulated. The weak and strong duality theorems are established under higher-order-invexity assumption. Symmetric minimax mixed integer primal and dual problems are also investigated.

On non-smooth α-invex functions and vector variational-like inequality

In this paper, we establish some relationships between vector variational-like inequality and non-smooth vector optimization problems under the assumptions of α-invex non-smooth functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality, under non-smooth pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends an earlier work of Ruiz-Garzon etxa0al. (J Oper Res 157:113–119, 2004) to a wider class of functions, namely the non-smooth pseudo-α-invex functions. Moreover, this work extends an earlier work of Mishra and Noor (J Math Anal Appl 311:78–84, 2005) to non-differentiable case.

Optimality and duality for a multi-objective programming problem involving generalized d-type-I and related n-set functions

In this paper, we introduce several generalized convexity for a real-valued set function and establish optimality and duality results for a multi-objective programming problem involving generalized d-type-I and related n-set functions.

ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, α-pseudo-univex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.

Second order symmetric duality for nonlinear multiobjective mixed integer programming

We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones. By using the concepts of efficiency and second order invexity, we establish weak, strong, converse and self-duality theorems for the dual models. Several known results are obtained as special cases.

Explicitly B-preinvex fuzzy mappings

We introduce the concept of an explicitly B-preinvex fuzzy mapping. Some properties of explicitly B-preinvex fuzzy mappings are also established. Further, various relationships between explicit B-preinvex fuzzy mappings and B-preinvex fuzzy mappings are established.

Optimality conditions for multiple objective fractional subset programming with (F, ρ,σ,θ )-V-type-I and related non-convex functions

In this paper, we introduce a new class of generalized convex n-set functions, called (, @r,@s,@q)-V-Type-I and related non-convex functions, and then establish a number of parametric and semi-parametric sufficient optimality conditions for the primal problem under the aforesaid assumptions. This work partially extends an earlier work of [G.J. Zalmai, Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (, @a, @r, @q)-V-convex functions, Comput. Math. Appl. 43 (2002) 1489-1520] to a wider class of functions.

Minimax programming under generalized (p, r)-invexity

Minimax programming problems involving generalized (p, r)-invex functions are considered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.