An inexact modified subgradient algorithm for nonconvex optimization

Authors:
Regina S. Burachik;C. Yalçın Kaya;Musa Mammadov
Affiliations:
Centre for Informatics and Applied Optimization, University of Ballarat, Victoria, Australia and School of Mathematics and Statistics, University of South Australia, Mawson Lakes, Australia 5095;School of Mathematics and Statistics, University of South Australia, Mawson Lakes, Australia 5095;Centre for Informatics and Applied Optimization, University of Ballarat, Victoria, Australia
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

We propose and analyze an inexact version of the modified subgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may allow to solve problems with less computational effort. We illustrate this through test problems, including an optimal bang-bang control problem, under several different inexactness schemes.