Some remarks on optimality conditions for fuzzy optimization problems

In this article we present a new concept of stationary point for gH-differentiable fuzzy functions which generalize previous concepts that exist in the literature. Also, we give a concept of generalized convexity for gH-differentiable fuzzy functions more useful than level-wise generalized convexity (generalized convexity of the endpoint functions). Then we give optimatily conditions for fuzzy optimization problems.En este artículo presentamos un nuevo concepto de punto estacionario para funciones difusas gHdiferenciables que generalizan los conceptos previos que existen en la literatura. También damos un concepto de convexidad generalizada para funciones difusas gH-diferenciables más útil que los basados en las funciones extremos. A partir de esos conceptos, damos condiciones de optimalidad para problemas de optimización difusos.Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Optimality and duality on Riemannian manifolds

Our goal in this paper is to translate results on function classes that are characterized by the property that all the Karush-Kuhn-Tucker points are efficient solutions, obtained in Euclidean spaces to Riemannian manifolds. We give two new characterizations, one for the scalar case and another for the vectorial case, unknown in this subject literature. We also obtain duality results and give examples to illustrate it.Ministerio de Economía y Competitivida

A reduced formulation for pseudoinvex vector functions

Vector pseudoinvexity is characterized in the current literature by means of a suitable functional which depends on two variables. In this paper, vector pseudoinvexity is characterized by means of a functional which depends on one variable only. For this very reason, the new characterizing conditions are easier to be verified

Solutions of Optimization Problems on Hadamard Manifolds with Lipschitz Functions

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush-Kuhn-Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash's critical and equilibrium points coincide in the case of invex payoff functions. This is done on Hadamard manifolds, a particular case of noncompact Riemannian symmetric spaces

Characterizations of the solution sets of pseudoinvex programs and variational inequalities

Author name used in this publication: Heungwing Lee2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

On the Subdifferentials of Quasiinvex and Pseudoinvex Functions and Cyclic Inmomocity

Abstract: The subdifferential characteristic of quasiinvex and pseudoinvex functions are vital role in convex optimization literature. Inmonicity and cyclic inmonicity properties are equally on the same line. In this paper, we studied the relation among subdifferential characteristics, inmonicity, and cyclic inmonicity of quasiinvex and pseudoinvex functions

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

The method of Weighted Multi objective Fractional Linear Programming Problem (MOFLPP)

More theories and algorithms in non-linear programming with titles convexity (Convex). When the objective function is fractional function, will not have to have any swelling, but can get other good properties have a role in the development of algorithms decision problem.In this work we focus on the weights method- (one of the classical methods to solve Multi objective convex case problem). Since we have no convex or no concave objective functions, and this condition is essential part on this method implementation, we these valid conditions under method as generator sets efficient and weakly efficient this problem. This raises the need to a detailed study of pseudoconvex idea, cause convex idea, Invex, pseudoinvex idea,…, etc. concepts. Offer a numerical example to show the valid by the conditions previously set generate all weakly efficient set our problem

Invexity and a Class of Constrained Optimization Problems in Hilbert Spaces

In this paper the notion of invexity has been introduced in Hilbert spaces. A class of constrained optimization problems has been proposed under the assumption of invexity. Some of the algebraic properties leading to the optimality criterion of such class of problems has been studied

Job shop scheduling with artificial immune systems

The job shop scheduling is complex due to the dynamic environment. When the information of the jobs and machines are pre-defined and no unexpected events occur, the job shop is static. However, the real scheduling environment is always dynamic due to the constantly changing information and different uncertainties. This study discusses this complex job shop scheduling environment, and applies the AIS theory and switching strategy that changes the sequencing approach to the dispatching approach by taking into account the system status to solve this problem. AIS is a biological inspired computational paradigm that simulates the mechanisms of the biological immune system. Therefore, AIS presents appealing features of immune system that make AIS unique from other evolutionary intelligent algorithm, such as self-learning, long-lasting memory, cross reactive response, discrimination of self from non-self, fault tolerance, and strong adaptability to the environment. These features of AIS are successfully used in this study to solve the job shop scheduling problem. When the job shop environment is static, sequencing approach based on the clonal selection theory and immune network theory of AIS is applied. This approach achieves great performance, especially for small size problems in terms of computation time. The feature of long-lasting memory is demonstrated to be able to accelerate the convergence rate of the algorithm and reduce the computation time. When some unexpected events occasionally arrive at the job shop and disrupt the static environment, an extended deterministic dendritic cell algorithm (DCA) based on the DCA theory of AIS is proposed to arrange the rescheduling process to balance the efficiency and stability of the system. When the disturbances continuously occur, such as the continuous jobs arrival, the sequencing approach is changed to the dispatching approach that involves the priority dispatching rules (PDRs). The immune network theory of AIS is applied to propose an idiotypic network model of PDRs to arrange the application of various dispatching rules. The experiments show that the proposed network model presents strong adaptability to the dynamic job shop scheduling environment.postprin