Invexity Assumptions Research Articles

Multi-objective infinite programming

Using the theory of abstract optimization problems in infinite-dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi-objective infinite programming problem. Sufficient conditions are given under invexity assumptions. We generalize the notion of KKT-invexity for the multi-objective infinite problem and show that this notion is a necessary and sufficient condition for every vector KKT solution to be a weakly efficient solution. Moreover, we develop a theorem of the alternative, useful for proving some of our results.

Optimality and duality for nonsmooth multiobjective fractional programming with mixed constraints

We consider nonsmooth multiobjective fractional programming problems with inequality and equality constraints. We establish the necessary and sufficient optimality conditions under various generalized invexity assumptions. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems.

Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions

In this paper, we discuss a fairly large number of nonparametric duality results under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.

Global Parametric Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.

Second order symmetric duality in multiobjective programming involving generalized cone-invex functions

In this paper, cone-second order pseudo-invex and strongly cone-second order pseudo-invex functions are defined. A pair of Mond–Weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are established under aforesaid generalized invexity assumptions. A second self-duality theorem is also given by assuming the functions involved to be skew-symmetric.

Global Nonparametric Sufficient Optimality Conditions for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.

Nonparametric Duality Models for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we discuss a fairly large number of nonparametric duality results under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.

A Modified Objective Function Method in Mathematical Programming with Second Order Invexity

A new approach for solving nonlinear constrained mathematical programming problems that makes use of second-order derivative is presented. In this method, a modified optimization problem associated with a primal nonlinear programming problem is constructed that involves second-order modified objective function constituting the primal problem. The equivalence between the nonlinear original mathematical programming problem and its associated optimization problem with a second-order modified objective function is established under second-order invexity assumption. In this way, the procedure for obtaining the second-order sufficient conditions for the mathematical programming problems of this type is presented.

Symmetric duality for a class of nondifferentiable multi-objective fractional variational problems

We introduce a symmetric dual pair for a class of nondifferentiable multi-objective fractional variational problems. Weak, strong, converse and self duality relations are established under certain invexity assumptions. The paper includes extensions of previous symmetric duality results for multi-objective fractional variational problems obtained by Kim, Lee and Schaible [D.S. Kim, W.J. Lee, S. Schaible, Symmetric duality for invex multiobjective fractional variational problems, J. Math. Anal. Appl. 289 (2004) 505–521] and symmetric duality results for the static case obtained by Yang, Wang and Deng [X.M. Yang, S.Y. Wang, X.T. Deng, Symmetric duality for a class of multiobjective fractional programming problems, J. Math. Anal. Appl. 274 (2002) 279–295] to the dynamic case.

Generalized (η,ρ)-Invex Functions and Global Semiparametric Sufficient Efficiency Conditions for Multiobjective Fractional Programming Problems Containing Arbitrary Norms

The purpose of this paper is to develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (η, ρ)-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

Generalized (η,ρ)-Invex Functions and Semiparametric Duality Models for Multiobjective Fractional Programming Problems Containing Arbitrary Norms

In this paper, we construct several semiparametric duality models and prove appropriate duality theorems under various generalized (η,ρ)-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

Infine functions and nonsmooth multiobjective optimization problems

In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions.

Sufficient optimality criteria and duality for multiobjective variational control problems with [formula omitted]-invexity

The sufficient optimality criteria for a class of multiobjective variational control problems under the V -invexity assumption are presented. Duality results are proved under a variety of V -invexity assumptions. Multiobjective fractional variational control problems are also studied.

NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient solution under suitable generalized invexity assumptions.

Some results on symmetric duality of multiobjective programmes with generalized ( F, ρ) invexity

In this present article we have given some multiobjective programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used most general type of invexity assumptions involved with the functions which are related to the programming problems. It is to be pointed out that the objective functions in such programs contain terms like support functions which in turn are able to give results on particular classes of programs involving quadratic terms. Our results in particular give as special cases some earlier results on symmetric duals given in the current literature.

Symmetric duality for multiobjective fractional variational problems with generalized invexity

The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized invexity assumptions. A close relationship between these problems and multiobjective fractional symmetric dual problems is also presented.

Generalized type I invexity and duality in multiobjective variational problems

In this paper, we introduce new classes of generalized V-type I invex functions for variational problems and consider a multiobjective variational problem (VP). A number of sufficiency results are established using Lagrange multiplier conditions under various types of generalized V-type I invexity requirements. Duality results are obtained for Mond–Weir type duals under the above generalized V-type I invexity assumptions and their generalizations.

Multiobjective duality withρ − (η, θ)‐invexity

Under ρ − (η, θ)‐invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

Minimax programming under ( p, r)-invexity

Minimax programming problems involving ( p, r)-invex functions with respect to η are considered. Parametric and non-parametric necessary and sufficient optimality conditions and duality results for a class of minimax programming problems are obtained under ( p, r)-invexity assumption on objective and constraint functions. Some different types of dual problems are introduced and duality theorems is established for each dual problem.

Optimality and Duality for Invex Nonsmooth Multiobjective programming problems

We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity assumptions and certain regularity conditions are presented. In addition, we introduce a Wolfe-type dual and Mond–Weir-type dual and establish duality relations under various (generalized) invexity and regularity conditions.