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

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.