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 Cádiz/CBUA. The research has been supported by MCIN through grant MCIN/AEI/PID2021-123051NB-I00

Some relations between Minty variational-like inequality problems and vectorial optimization problems in Banach spaces

This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach spaces under pseudo-invexity and pseudo-monotonicity hypotheses. We have extended the results given by Gang and Liu (2008) [22] to Banach spaces and the relationships obtained for weak efficient points in Santos et al. (2008) [21] are completed and enabled to relate vector critical points, weak efficient points, solutions of the Minty and Stampacchia weak vector variationallike inequalities problems and solutions of perturbed vector variational-like inequalities problems

Algumas contribuições em controle ótimo discreto

Orientadora : Profª. Drª. Lucelina Batista dos SantosCoorientador : Prof. Dr. Marko Antonio Rojas MedarTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Matemática. Defesa: Curitiba, 25/08/2017Inclui referências : f. 133-139Resumo: Neste trabalho consideramos os problemas de controle .timo discretos com um e com vários objetivos, nos casos regulares e 2 regulares. Este estudo esta dividido em tr.s frentes: a primeira trata das condições de otímalidade destes dois tipos de problemas em suas versões mono e multiobjetivo. Nesta parte apresentamos uma versão do Princípio do Maximo Discreto e introduzimos conceitos de invexidade nos quais, os problemas PM-invexos e PM-pseudoinvexos são a chave para garantir a suficiência destas condições para o caso regular. Na segunda, discutimos os conceitos de estabilidade e sensibilidade a certos problemas de controle ótimo discretos escalares, para os quais obtivemos dois resultados importantes envolvendo condições de crescimento quadrático, independência linear e 2 regularidade. Já na ultima parte, abordamos a otimalidade de um certo problema de controle ótimo discreto multiobjetivo não diferençável. Através do conceito de diferenciabilidade generalizada de Clarke, apresentamos uma versão do Princípio do Máximo para tal problema. Palavras-chave: Controle Ótimo Discreto; Principio do Maximo Discreto; PM-invexidade,Abstract: In this Thesis, we discuss discrete optimal control problems for regular and irregular (2 regular) cases. This study was divided into three fronts: the first deals with the optimality conditions of these two types of problems in their scalar and multiobjective versions. In this part we present a version of the Discrete Maximum Principle and we introduce the concepts of MP-invexity and MP-pseudoinvexity for these problems; these notions were the key to guarantee the adequacy of these conditions for regular problems. In the second part, we discuss the concepts of stability and sensitivity for certain discrete scalar control problems, for which we obtained two important results involving quadratic growth conditions, linear independence and regularity. In this last part, we discuss the optimality of a certain class of nonsmooth discrete multiobjective optimal control problems. Based on Clarke's concept of generalized differentiability, we present a version of the Principle of Maximum. Keywords: Discrete Optimal Control, Maximum Principle, MP-invexity, 2 regularity, Stability and Sensibility, Nonsmooth

UN APPROCCIO DINAMICO AI PROBLEMI DI OTTIMIZZAZIONE VETTORIALE

2000/2001XIII Ciclo1969Versione digitalizzata della tesi di dottorato cartacea

CONCAVITA' GENERALIZZATA: CASO SCALARE E CASO VETTORIALE

1993/1994VII Ciclo1968Versione digitalizzata della tesi di dottorato cartacea. Nell'originale cartaceo errata numerazione delle pagin

Public Facility Location: Issues and Approaches

The papers collected in this issue were presented at the Task Force Meeting on Public Facility Location, held at IIASA in June 1980. The meeting was an important occasion for scientists with different backgrounds and nationalities to compare and discuss differences and similarities among their approaches to location problems. Unification and reconciliation of existing theories and methods was one of the leading themes of the meeting, and the papers collected here are part of the raw material to be used as a starting point towards this aim. The papers themselves provide a wide spectrum of approaches to both technical and substantive problems, for example, the way space is treated (continuously in Beckmann, in Mayhew, and in Thisse et al, discretely in all the others), the way customers are assigned to facilities (by behavioral models in Ermoliev and Leonardi, in Sheppard, and in Wilson, by normative rules in many others), the way the objective function is defined (ranging from total cost, to total profit, total expected utility for customers, accessibility, minimax distance, maximum covering, to a multi-objective treatment of all of them as in Revelle et al. There is indeed room for discussion, in order to find both similarities and weaknesses in different approaches. A general weakness of the current state of the art of location modeling may also be recognized: its general lack of realism relative to the political and institutional issues implied by locational decisions. This criticism, developed by Lea, might be used both as a concluding remark and as a proposal for new challenging research themes to scholars working in the field of location theory