Higher order symmetric duality in nondifferentiable multi-objective programming problems involving generalized cone convex functions

Nondifferentiable multiobjective symmetric duality with [formula omitted]-convexity over cones

This paper deals with non-differentiable multi-objective semi-infinite programming problem. It is a problem of simultaneous minimisation of finitely many scalar valued functions subject to an arbitrary (possibly infinite) set of constraints. Non-differentiability enters, due to the square root of a quadratic form which appears in the objective functional. Concept of efficiency of order m has been extended to the above stated problem. In order to study this new solution concept, the notion of ρ-invexity of order m is also proposed which is utilised to establish sufficient optimality conditions for the non-differentiable multi-objective semi-infinite programming problem. Mond-Weir type of dual is proposed for which weak, strong and strict converse duality theorems are established.

In this paper, a pair of non-differentiable second-order multi-objective symmetrical dual fractional variational programs over arbitrary cones is constructed. We have introduced the concept of second-order (F, α, ρ, d)-pseudoconvexity and an example of a function which is second-order (F, α, ρ, d)-pseudoconvex but not second-order F-pseudoconvex has been constructed. Further, to relate the objective function value of primal and dual, we proved weak, strong, and converse duality theorems under second-order (F, α, ρ, d)-pseudoconvexity suppositions. Moreover, to validate the results of the weak duality theorem, an example of a multi-objective variational fractional problem and its dual model has been constructed. Several known results are also discussed as special cases.

Two different pairs of higher-order symmetric dual programs such as Wolfe type and Mond–Weir type are studied. The weak, strong and converse duality theorems are established for the higher-order symmetric dual programs under higher-order \(\rho -(\eta ,\theta )-\)invexity and \(\rho -(\eta ,\theta )-\)pseudo-invexity assumptions. Many examples and counterexamples are illustrated to justify our work. We also observe that several known results are obtained as special cases.

Higher-order symmetric duality in vector optimization problem involving generalized cone-invex functions

In this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.

We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.

Multiobjective second order symmetric duality with cone constraints

Minimax fractional programming under nonsmooth generalized [formula omitted]-d-univexity

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

This article gives some new duality results for the multitime control optimization problem with data uncertainty (MCOPU). We formulate Wolfe and Mond‐Weir type robust dual problems for (MCOPU) and prove the weak robust duality theorem which states that the duality gap is positive and the strong robust duality theorem which shows the zero duality gap under convexity assumptions. Further, we also prove the converse robust duality result. Moreover, we give some nontrivial examples to verify the established results in this article.

In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems are also derived for Mond-Weir type multiobjective dual programs.

In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem.

Duality for nondifferentiable minimax programming in complex spaces

ABSTRACTIn this paper, a second-order dual problem for a non-differentiable minimax complex programming problem is formulated. The weak, strong, and strict converse duality theorems are constructed under generalized Θ-bonvexity assumptions. This means that there are no duality gaps between primary problem and its dual problem.