Abstract
Methods are considered for solving nonlinear programming problems using an exactl 1 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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Fletcher, R., de la Maza, E.S. Nonlinear programming and nonsmooth optimization by successive linear programming. Mathematical Programming 43, 235–256 (1989). https://doi.org/10.1007/BF01582292
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DOI: https://doi.org/10.1007/BF01582292