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SQP Methods for Parametric Nonlinear Optimization

Vyacheslav Kungurtsev (vyacheslav.kungurtsev***at***cs.kuleuven.be)
Moritz Diehl (moritz.diehl***at***esat.kuleuven.be)

Abstract: Sequential quadratic programming (SQP) methods are known to be effi- cient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties–a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere with the potential to take advantage of these theoretical local properties in full. We present two new predictor-corrector procedures for solving a nonlinear program given a suf- ficiently accurate estimate of a similar problem. The procedures attempt to trace a homotopy path between solutions of the two problems, staying within the local domain of convergence for the series of problems generated. We provide theoretical convergence and tracking results, as well as some numerical results demonstrating the robustness and performance of the methods.

Keywords: Parametric nonlinear programming, Nonlinear programming, nonlinear constraints, sequential quadratic program-ming, SQP methods, stabilized SQP, homotopy, continuation methods, model predictive control

Category 1: Nonlinear Optimization

Citation: KULeuven ESAT STADIUS Internal Report Number 14-34 Submitted to Computational Optimization and Applications

Download: [PDF]

Entry Submitted: 02/28/2014
Entry Accepted: 02/28/2014
Entry Last Modified: 07/07/2014

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