Nonlinear programming and nonsmooth optimization by successive linear programming |
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Authors: | R. Fletcher E. Sainz de la Maza |
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Affiliation: | (1) Department of Mathematical Sciences, University of Dundee, Scotland, England;(2) Department of Applied Mathematics, Universidad del Pais Vasco, Bilbao, Spain |
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Abstract: | Methods are considered for solving nonlinear programming problems using an exactl1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence. In one particular method, second order information is represented by approximating the reduced Hessian matrix, and Coleman-Conn steps are taken. A criterion for accepting these steps is given which enables the superlinear convergence properties of the Coleman-Conn method to be retained whilst preserving global convergence and avoiding the Maratos effect. The methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting. A range of numerical experiments on small test problems is described. |
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Keywords: | Nonlinear programming nonsmooth optimization global convergence superlinear convergence trust region method Coleman-Conn method |
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