Nonlinear programming and nonsmooth optimization by successive linear programming

Nonlinear programming and nonsmooth optimization by successive linear programming

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Article ID: iaor19881246
Country: Netherlands
Volume: 43
Issue: 3
Start Page Number: 235
End Page Number: 256
Publication Date: Apr 1989
Journal: Mathematical Programming (Series A)
Authors: ,
Abstract:

Methods are considered for solving nonlinear programming problems using an exact l1 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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