Parametric approach for a class of fractional variational programs involving support functions

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

In this work, we introduce a pair of multiobjective second-order symmetric dual variational problems. Weak, strong, and converse duality theorems for this pair are established under the assumption of ?-bonvexity/?-pseudobonvexity. At the end, the static case of our problems has also been discussed.

Multiobjective second order symmetric duality with cone constraints

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

In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, we formulate and prove weak, strong, and converse duality theorems under (ϱ,ψ,ω)-quasiinvexity hypotheses for the considered class of optimization problems.

We establish the necessary and sufficient optimality conditions on a nondifferentiable minimax fractional programming problem. Subsequently, applying the optimality conditions, we constitute two dual models: Mond-Weir type and Wolfe type. On these duality types, we prove three duality theorems--weak duality theorem, strong duality theorem, and strict converse duality theorem.

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 work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (?, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.

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.

We suggest a pair of symmetric dual nonlinear programs which can be reduced to that of Mond, originally formulated by Dantzig, Eisenberg and Cottle, and to that of Mond and Weir. The weak, strong and converse duality theorems for our programs are established. The first and second authors were supported in part by the Research Institute Attached to University Program, Korea Research Foundation (1993). The third author was supported in part by the Basic Science Research Institute Program, Ministry of Education, Korea, 1995, Project No. BSRI-95–1405.

Duality for nondifferentiable minimax programming in complex spaces

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.

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.

This article delves into the analysis of semi-infinite multi-objective optimization problems characterized by constraints that gradually vanish. We establish sufficient efficiency criteria to determine whether a feasible solution attains a Pareto solution in the given multi-objective optimization problem considering the presence of vanishing constraints and suitable generalized convexity assumptions. We provide illustrative examples to confirm the validity of our findings. Additionally, we derive weak, converse, strong converse, and strong duality theorems for a dual model based on Mond–Weir principles, relying on generalized convexity assumptions.

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained set-valued optimization problem, respectively. Then, corresponding weak duality, strong duality, and converse duality theorems are established.