A Flexible Inexact-Restoration Method for Constrained Optimization

L. F. Bueno (), G. Haeser () and J. M. Martínez ()
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L. F. Bueno: Federal University of São Paulo
G. Haeser: University of São Paulo
J. M. Martínez: University of Campinas

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 1, No 9, 188-208

Abstract: 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.

Keywords: Nonlinear programming; Inexact-restoration; Global convergence; Lagrange multipliers; 90C30; 49K99; 65K05 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-014-0572-0

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