Duality in Nondifferentiable Vector Programming

AbstractIn this paper we study the saddle point optimality conditions and Lagrange duality in multiobjective optimization for generalized subconvex-like functions. We obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined. We also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem

Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces

AbstractIn this work, we introduce the notion of preinvex function for functions between Banach spaces. By using these functions, we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities. Moreover, we will show that this class of problems has the property that each local optimal solution is in fact global

A necessary and sufficient condition for duality in multiobjective variational problems

In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn-Tucker or Fritz John points are efficient solutions. Recent papers are improved. We provide an example to show this improvement and illustrate these classes of functions and results.Multiple objective programming Nonlinear programming Multiobjective variational problem Pseudoinvexity Optimality condition

Multiobjective fractional programming with generalized convexity

Multiobjective fractional programming problem, weakly efficient solution, generalized convexity, 90C30, 90C25,