On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems

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.

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.

In this paper, we extend the notions of $$(\Phi ,\rho )$$ ( ? , ? ) -invexity and generalized $$(\Phi ,\rho )$$ ( ? , ? ) -invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under $$(\Phi ,\rho )$$ ( ? , ? ) -invexity.

In the paper, we introduce the concepts of $$G$$ -type I and generalized $$G$$ -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are $$G$$ -type I and/or generalized $$G$$ -type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) $$G$$ -type I objective and constraint functions.

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.

In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.

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.

On symmetric gH-derivative: Applications to dual interval-valued optimization problems

In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established. Our study naturally unifies and extends some previously known results on minimax programming.

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.

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.

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

Wolfe and Mond-Weir type duals for multiobjective variational problems are formulated.Under pseudo-invexity assumption on the functions involved Weak and converse duality theorems are proved to relate efficient solutions/properly efficient solutions of the primal and dual problems. A close relationship between these variational problems and non-linear multiobjective prograrnmlng problems is also indicatcd

This paper investigates a class of multi-objective variational control problems, named (VCP), characterized by vector-valued integral objective/cost functional and differentiable inequality constraints. More precisely, we formulate the problem in a general framework and, in order to analyze optimality criteria, we associate scalar subproblems with the multi-objective setting and establish conditions under which efficient solutions of the original vector problem correspond to optimal solutions of these scalarized problems. We derive the necessary optimality conditions in the form of Euler–Lagrange-type equations, involving multipliers and piecewise smooth functions as variables. Furthermore, we introduce the new notion of (ϵ0, ϵ1) − (c0, c1) − type − I pair of functionals, adapted to the variational control setting. The introduced generalized convexity concepts are very important in characterizing efficient solutions and in deriving enhanced optimality conditions. These results enrich the theoretical framework of multi-objective variational control and provide a solid basis for future research and applications in mathematical optimization and control theory.

Duality for nondifferentiable minimax programming in complex spaces