Variational inequalities theory has been widely used in many fields, such as economics, physics, engineering, optimization and control, transportation [1, 4]. Like convexity to mathematical programming problem (MP), monotonicity plays an important role in solving variational inequality (VI). To investigate the variational inequality, many kinds of monotone mappings have been introduced in the l...

In this paper are defined new firstand second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds b...

In this paper we have considered a non convex optimal control problem and presented the weak, strong and converse duality theorems. The optimality conditions and duality theorems for fractional generalized minimax programming problem are established. With a parametric approach, the functions are assumed to be pseudo-invex and v-invex.

for Invex Programs via Penalty Functions J. Zhang Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China X. X. Huang School of Management, Fudan University, Shanghai 200433, China Abstract. In this paper, we apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program....

In this paper, we define and introduce some new concepts of strongly φ-preinvex (φ-invex) functions and strongly φη-monotone operators. We establish some new relationships among various concepts of φ-preinvex (φ-invex) functions. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previous...

In this paper we obtain secondand first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable. We introduce notions of KTSP-invex problem and second-order KTSP-invex one. We obtain that t...

In this paper, a class of generalized invex functions, called [Formula: see text]-invex functions, is introduced, and some examples are presented to illustrate their existence. Then we consider the relationships of solutions between two types of vector variational-like inequalities and multi-objective programming problem. Finally, the existence results for the discussed variational-like inequal...

This paper addresses the problem of capturing nondominated points on convex Pareto frontiers, which are encountered in invex multi-objective programming problems. An algorithm to find a piecewise linear approximation of the nondominated set of convex Pareto frontier are applied. Index Term-Approximation, Nondominated points, Invex multi-objective problems, Block norms.

⎯ The aim of the present work is to characterize weakly efficient solution of multiobjective programming problems under the assumptions of α-invexity, using the concepts of critical point and Kuhn-Tucker stationary point for multiobjective programming problems. In this paper, we also extend the above results to the nondifferentiable multiobjective programming problems. The use of α-invex functi...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...