Optimization with LOVO constraints, inexact restoration and the inverse Nash equilibrium

Author(s)

Luís Felipe Cesar da Rocha Bueno

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2011-09-27

Examining board members

José Mario Martínez Pérez; Roberto Andreani; Sandra Augusta Santos; Ernesto Julián Goldberg Birgin; Gabriel Haeser

• Advisor: José Mario Martínez Pérez

Abstract

In this work an Augmented Lagrangian method will be proposed to deal with LOVO constraints, also some new Inexact Restoration methods will be presented and the Inverse Nash Equilibrium concept will be introduced. Theorems about optimality conditions for LOVO-like problems will be presented. Three Augmented Lagrangian algorithms will be proposed to approach this problem and global convergence theorems will be proved. Computational results will be performed for an application in portfolio optimization with impact. A modification of the Fischer-Friedlander global method using the Sharp Lagrangian as a merit function will be proposed. A hybrid Inexact Restoration method combining this modification and the Birgin-Martínez local method will be introduced. Global and local convergence theorems will be presented. An Inexact Restoration method for problems in which the derivatives of the objective function are not available will be introduced. In this method it will be used all the optimization traditional tools in the restoration process as well as a regularization strategy in the optimization phase. Global convergence theorems will be demonstrated and numerical results will be presented. The concept of Inverse Nash Equilibrium will be introduced and an Inexact Restoration method will be proposed to deal with this problem. This method is an extension of a new Inexact Restoration method for bilevel programming that will also be proposed in this work. Some illustrative examples for an application for the Arrow- Debreu equilibrium problem will be given (AU)

• FAPESP's process: 07/06663-0 - Order value optimization applied to inverse Nash-Equilibrium
• Grantee: Luis Felipe Cesar da Rocha Bueno
• Support Opportunities: Scholarships in Brazil - Doctorate