A Flexible Inexact-Restoration Method for Constrained Optimization

Author(s)

Bueno, L. F. ^[1] ; Haeser, G. ^[2] ; Martinez, J. M. ^[3]

Affiliation

^[1] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil

^[2] Univ Sao Paulo, Inst Math & Stat, Dept Appl Math, Sao Paulo, SP - Brazil

^[3] Univ Estadual Campinas, Inst Math Stat & Sci Comp, Dept Appl Math, Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 165, n. 1, p. 188-208, APR 2015.
• Web of Science Citations: 3

Abstract

We introduce a new flexible inexact-restoration algorithm for constrained optimization problems. In inexact-restoration methods, each iteration has two phases. The first phase aims at improving feasibility and the second phase aims to minimize a suitable objective function. In the second phase, we also impose bounded deterioration of the feasibility, obtained in the first phase. Here, we combine the basic ideas of the Fischer-Friedlander approach for inexact-restoration with the use of approximations of the Lagrange multipliers. We present a new option to obtain a range of search directions in the optimization phase, and we employ the sharp Lagrangian as merit function. Furthermore, we introduce a flexible way to handle sufficient decrease requirements and an efficient way to deal with the penalty parameter. Global convergence of the new inexact-restoration method to KKT points is proved under weak constraint qualifications. (AU)

• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 10/19720-5 - Optimality conditions and inexact restoration
• Grantee: Gabriel Haeser
• Support Opportunities: Research Grants - Young Investigators Grants