22 research outputs found
Decision analysis: vector optimization theory
First published in Revista de la Real Academia de Ciencias Exactas, F铆sicas y Naturales in 93, 4, 1999, published by the Real Academia de Ciencias Exactas, F铆sicas y Naturales
On the Newton method for solving fuzzy optimization problems
In this article we consider optimization problems where the objectives are fuzzy functions (fuzzy-valued functions). For this class of fuzzy optimization problems we discuss the Newton method to find a non-dominated solution. For this purpose, we use the generalized Hukuhara differentiability notion, which is the most general concept of existing differentiability for fuzzy functions. This work improves and correct the Newton Method
previously proposed in the literature.Fondo Nacional de Desarrollo Cient铆fico y Tecnol贸gico (Chile)Ministerio de Ciencia y Tecnolog铆aConselho Nacional de Desenvolvimento Cient铆fico e Tecnol贸gico (Brasil)Centro de Pesquisa em Matem谩tica Aplicada 脿 Ind煤stria (Funda莽茫o de Amparo 脿 Pesquisa do Estado de S茫o Paulo
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
Semi-infinite interval equilibrium problems: optimality conditions and existence results
This paper aims to obtain new Karush鈥揔uhn鈥揟ucker optimality conditions for solutions
to semi-infinite interval equilibrium problems with interval-valued objective functions. The
Karush鈥揔uhn鈥揟ucker conditions for the semi-infinite interval programming problem are
particular cases of those found in this paper for constrained equilibrium problem.We illustrate
this with some examples. In addition, we obtain solutions to the interval equilibrium problem
in the unconstrained case. The results presented in this paper extend the corresponding results
in the literature.The research has been supported by FEDER Andaluc铆a 2014-2020 (UPO-1381297) and by MICIN through grant MCIN/AEI/PID2021-123051NB-100
Second-order optimality conditions for interval-valued functions
This work is included in the search of optimality conditions for solutions to the scalar
interval optimization problem, both constrained and unconstrained, by means of
second-order optimality conditions. As it is known, these conditions allow us to reject
some candidates to minima that arise from the first-order conditions. We will define
new concepts such as second-order gH-derivative for interval-valued functions,
2-critical points, and 2-KKT-critical points. We obtain and present new types of
interval-valued functions, such as 2-pseudoinvex, characterized by the property that
all their second-order stationary points are global minima. We extend the optimality
criteria to the semi-infinite programming problem and obtain duality theorems.
These results represent an improvement in the treatment of optimization problems
with interval-valued functions.Funding for open access publishing: Universidad de C谩diz/CBUA. The research has been supported by MCIN through
grant MCIN/AEI/PID2021-123051NB-I00
FJ-Invex control problem
This paper introduces a new condition on the functionals of a control problem and extends
a recent characterization result of KT-invexity. We prove that the new condition, the FJinvexity, is both necessary and sufficient in order to characterize the optimal solution set
using Fritz John points
Generalized convexity: Their applications to variational problems
The aim of this paper is to show one of the generalized convexity applications, generalized monotonicity particularly, to the variational problems study. These problems are related to the search of equilibrium conditions in physical and economic environments. If convexity plays an important role in mathematical programming problems, monotonicity will play a similar role in variational problems. This paper shows some recent results about this topic
Generalized convexity: Their applications to multiobjective programming
The aim of this paper is to show some applicable results to multiobjective
optimization problems and the role that the Generalized Convexity plays in them. The study of convexity for sets and functions has special relevance in the search of optimal functions, and in the development of algorithms for solving optimization problems. However, the absence of convexity implies a total loss of effectiveness of the Optimization Theory methods, ie, the results are being verified under less stringent conditions, it was what became known as Generalized convexity. The literature generated around this topic has demonstrated its importance both from a theoretical point of view as practical, but it has also generated an enormous amount of papers with little scientific input