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An Implementation of an Algorithm for Nonlinear Programming Based on Piecewise Linear Models

Richard Byrd(Richard.Byrd***at***colorado.edu)
Jorge Nocedal(nocedal***at***eecs.northwestern.edu)
Richard Waltz(richard.waltz***at***gmail.com)
Yuchen Wu(rainson.wood***at***gmail.com)

Abstract: This is a progress report on an implementation of the active-set method for nonlinear programming proposed in [6] that employs piecewise linear models in the active-set prediction phase. The motivation for this work is to develop an algorithm that is capable of solving large-scale problems, including those with a large reduced space. Unlike SQP methods, which solve a general quadratic program at each iteration, the proposed algorithm solves linear programs and equality constrained quadratic programs -- both of which scale up well in the number of variables and constraints. The algorithm is implemented in the Knitro software package and contains a variety of features to handle difficulties occurring in practice, such as Jacobian rank deficiencies, infeasibility, and ill-conditioning. Particular attention is given to the implementation of the piecewise linear models to achieve economy of computation and to conform with the theoretical guidelines given in [6]. Numerical results comparing the new algorithm with two established active-set solvers, Snopt and Knitro/Active, are presented.

Keywords: constrained optimization, nonlinear programming

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 04/21/2011
Entry Accepted: 04/21/2011
Entry Last Modified: 04/21/2011

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