Invexity Assumptions Research Articles

MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

An η-Approximation Approach for Nonlinear Mathematical Programming Problems Involving Invex Functions

A new approach to a solution of a nonlinear constrained mathematical programming problem and its Mond–Weir duals is introduced. An η-approximated problem associated with a primal nonlinear programming problem is presented that involves η-approximated functions constituting the primal problem. The equivalence between the original mathematical programming problem and its associated η-approximated optimization problem is established under invexity assumption. Furthermore, η-approximated dual problems in the sense of Mond–Weir are introduced for the obtained η-approximated optimization problem in this method. By the help of η-approximated dual problems some duality results are established for the original mathematical programming problem and its original duals.

Symmetric duality for invex multiobjective fractional variational problems

We introduce a symmetric dual for multiobjective fractional variational problems. Under certain invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. The paper includes an extension of previous symmetric duality results for the static case obtained by Weir to the dynamic case.

Second-order duality for the variational problems

A dual problem associated with a class of variational problems is formulated that involves second derivatives of the functions. Under the invexity assumptions on the functions that compose the primal problems, second-order duality results (weak duality, strong duality and converse duality) are derived for this pair of problems.

Generalized Symmetric Duality for Multiobjective Variational Problems with Invexity

We formulate a pair of multiobjective nonlinear generalized symmetric dual variational problems involving vector-valued functions which unify the Wolfe and Mond–Weir models. For a special case, our problems become the symmetric dual pair of D. S. Kim and W. J. Lee (1998, J. Math. Anal. Appl. 218, 34–48). Under invexity assumptions, we establish weak, strong, and converse duality theorems for our variational problems by using the concept of efficiency. Also, we give the static case of our multiobjective generalized symmetric duality results. Several known results are obtained as special cases.

On multiobjective generalized symmetric dual programs withρ − (η, θ)-invexity

A pair of multiobjective generalized symmetric dual nonlinear programming problems and weak, strong and converse duality theorems for these problems are established under generalized ρ − (η, θ)-invexity assumptions. Several known results are obtained as special cases.

Symmetric Duality for Multiobjective Variational Problems with Invexity

We formulate a pair of multiobjective nonlinear symmetric dual variational problems. For the single objective problems our problems become the symmetric dual pair of I. Smart and B. Mond (J. Math. Anal. Appl.152, 1990, 536–545). Under invexity assumptions, we establish the weak, strong, converse, and self duality theorems for our variational problems by using the concept of efficiency. Also, we give the static case of our symmetric duality results.

Multiobjective symmetric duality with invexity

Usual duality results are proved for Wolfe and Mond-Weir type multiobjective symmetric dual problems without nonnegativity constraints under invexity/generalised invexity assumptions. Moreover, assuming the kernel function to be skew symmetric, the multiobjective problems are exhibited to be self duals.

Generalized symmetric duality with invexity in variational problems

We formulate a pair of generalized symmetric variational problems. Weak, strong and converse duality theorems are established under invexity assumptions for these problems. Also, we give the static case of our generalized symmetric duality results. Several known results are obtained as special cases.

Duality for Multiobjective Variational Problems with Invexity

In this paper, Wolfe and Mond–Weir type duals for a class of nondifferentiable multiobjective variational problems are formulated. Under invexity assumptions on the objective and the constraint functions involved, weak and strong duality theorems are proved to related properly efficient solutions for primal and dual problems. Later, related problems with these variational problems are introduced.

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

Generalized Continuous Nondifferentiable Fractional Programming Problems with Invexity

The concept of invexity has allowed the convexity requirements in a variety of mathematical programming problems to be weakened. We extend a number of Kuhn-Tucker type sufficient optimality criteria for a class of continuous nondifferentiable minmax fractional programming problems that involves several ratios in the objective with a nondifferentiable term in the numerators. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalized invexity assumptions. These results extend many well-known duality results and also give a dynamic generalization of those of finite dimensional nonlinear programming problems recently explored.

Optimality criteria and duality in multiple-objective optimization involving generalized invexity

A multiple-objective optimization problem involving generalized invex functions is considered. Kuhn-Tucker type necessary and sufficient conditions are obtained for a feasible point to be an efficient or properly efficient solution. Two dual programs are obtained. The results are given under weaker invexity assumptions.

Sufficient optimality criteria and duality for variational problems with generalised invexity

AbstractA number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.