C. Nahak

Duality for multiobjective variational problems with invexity

Wolfe and Mond-Weir type duals for multiobjective variational problems are formulated. Under invexity assumptions 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 nonlinear multiobjective programming problems is also indicated

Nonsmooth ρ − (η, θ)-invexity in multiobjective programming problems

In this paper we extend Reiland’s results for a nonlinear (single objective) optimization problem involving nonsmooth Lipschitz functions to a nonlinear multiobjective optimization problem (MP) for ρ − (η, θ)-invex functions. The generalized form of the Kuhn–Tucker optimality theorem and the duality results are established for (MP).

Duality for Variational Problems with Pseudo-Invexity

In this paper the duality results of Mond, Chandra and Husain for variational problems are extended to generalized invex (pseudo-invex) functions

Optimality conditions and duality for multiobjective variational problems with generalized ρ-(η, θ)-B-type-I functions

We use ρ - (η, θ)-B-type-I and generalized ρ - (η, θ)-B-type-I functions to establish sufficient optimality conditions and duality results for multiobjective variational problems. Some of the related problems are also discussed.

Higher-order symmetric duality in multiobjective programming problems under higher-order invexity

Abstract In this paper we present a pair of Wolfe and Mond–Weir type higher-order symmetric dual programs for multiobjective symmetric programming problems. Different types of higher-order duality results (weak, strong and converse duality) are established for the above higher-order symmetric dual programs under higher-order invexity and higher-order pseudo-invexity assumptions. Also we discuss many examples and counterexamples to justify our work.

An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems

In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions.

Approximation solvability of a class of A-monotone implicit variational inclusion problems in semi-inner product spaces

Abstract This paper deals with the existence of solutions for a class of nonlinear implicit variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of implicit variational inclusions problems involving A -monotone and H -monotone operators by using the generalized resolvent operator technique.

Second-Order Symmetric Duality with Generalized Invexity

A pair of second-order symmetric dual programs such as Wolfe-type and Mond—Wier-type are considered and appropriate duality results are established. Second-order ρ − (η,θ)-bonvexity and ρ − (η,θ)-boncavity of the kernel function are studied. It is also observed that for a particular kernel function, both these pairs of programs reduce to general nonlinear problem introduced by Mangasarian. Many examples and counterexamples are illustrated to justify our work.

Application of the penalty function method to generalized convex programs

We use the penalty function method to study duality in generalized convex (invex) programming. In particular, we will obtain a new derivation under which the generalized convex (invex) programs do not have duality gaps.

Some new generalizations of Hardy's integral inequality

We have studied some new generalizations of Hardys integral inequality using the generalized Holders inequality.