25 research outputs found
On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions
A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)−ρ −(η,θ)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved
Necessary Optimality Conditions for Continuous-Time Optimization Problems with Equality and Inequality Constraints
The paper is devoted to obtain first and second order necessary optimality
conditions for continuous-time optimization problems with equality and
inequality constraints. A full rank type regularity condition along with an
uniform implicit function theorem are used in order to establish such necessary
conditions.Comment: 20 page
Multiobjective Programming under Generalized Type I Invexity
AbstractIn this paper we extend a (scalarized) generalized type-I invexity into a vector invexity (V-type I). A number of sufficiency results are established using Lagrange multiplier conditions and under various types of generalized V-type I requirements. Weak, strong, and converse duality theorems are proved in the generalized V-invexity type I setting
Continuous-Time Multiobjective Optimization Problems via Invexity
We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and
Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we
show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution
to be a weakly efficient solution
Duality in Minimax Fractional Programming Problem Involving Nonsmooth Generalized (F, α, ρ, d)-Convexity
Abstract: In this paper, we discuss nondifferentiable minimax fractional programming problem where the involved functions are locally Lipschitz. Furthermore, weak, strong and strict converse duality theorems are proved in the setting of Mond-Weir type dual under the assumption of generalized (F, α, ρ, d)-convexity
The continuous-time problem with interval-valued functions: applications to economic equilibrium
The aim of this paper is to define the Continuous-Time Problem
in an interval context and to obtain optimality conditions for this
problem. In addition, we will find relationships between solutions
of Interval Continuous-Time Problem (ICTP) and Interval Variationallike
Inequality Problems, both Stampacchia and Minty type. Pseudo
invex monotonicity condition ensures the existence of solutions
of the (ICTP) problem. These results generalize similar conclusions
obtained in Euclidean or Banach spaces inside classical mathematical
programming problems or Continuous-Time Problems. We will finish
generalizing the existence of Walrasarian equilibrium price model
and the Wardrop’s principle for traffic equilibrium problem to an
environment of interval-valued functions.The research in this paper has been partially supported by Ministerio de Economía y Competitividad,
Spain, through grant MTM2015-66185-P and Proyectos I+D 2015 MTM2015-66185-P
(MINECO/FEDER) and Fondecyt, Chile, grant 1151154
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
This paper contains selected applications of the new tangential extremal
principles and related results developed in Part I to calculus rules for
infinite intersections of sets and optimality conditions for problems of
semi-infinite programming and multiobjective optimization with countable
constraint