Topics in differentiable exact penalties

Author(s)

Ellen Hidemi Fukuda

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2011-03-11

Examining board members

Paulo José da Silva e Silva; Roberto Andreani; Carlos Humes Junior; Elizabeth Wegner Karas; José Mario Martinez Perez

• Advisor: Paulo José da Silva e Silva

Abstract

During the 1970\'s and 1980\'s, methods based on differentiable exact penalty functions were developed to solve constrained optimization problems. One drawback of these functions is that they contain second-order terms in their gradient\'s formula, which do not allow the use of Newton-type methods. To overcome such difficulty, we use an idea for construction of exact penalties for variational inequalities, introduced recently by André and Silva. This construction consists on incorporating a multipliers estimate, proposed by Glad and Polak, in the augmented Lagrangian function for variational inequalities. In this work, we extend the multipliers estimate to deal with both equality and inequality constraints and we weaken the regularity assumption. As a result, we obtain a continuous differentiable exact penalty function and a new equation reformulation of the KKT system associated to nonlinear problems. The formula of such reformulation allows the use of semismooth Newton method, and the local superlinear convergence rate can be also proved. Besides, we note that the exact penalty function can be used to globalize the method, resulting in a Gauss-Newton-type approach. We conclude with some numerical experiments using the collection of test problems CUTE. (AU)

• FAPESP's process: 07/53471-0 - Topics in differentiable exact penalties
• Grantee: Ellen Hidemi Fukuda
• Support Opportunities: Scholarships in Brazil - Doctorate