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IMA Journal of Numerical Analysis Advance Access published online on March 14, 2008
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn003
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Flexible penalty functions for nonlinear constrained optimization

Dedicated to Prof. M. J. D. Powell, pioneer of nonlinear optimization, on occasion of his 70th birthday

Frank E. Curtis{dagger}

Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208-3118, USA

Jorge Nocedal

Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208-3118, USA
{dagger} Email: fecurt{at}gmail.com

Received on 11 April 2007. Accepted for publication 5 January 2007.


  Abstract

We propose a globalization strategy for nonlinear constrained optimization. The method employs a ‘flexible’ penalty function to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. This increased flexibility in the step acceptance procedure is designed to promote long productive steps for fast convergence. An analysis of the global convergence properties of the approach in the context of a line search sequential quadratic programming method and numerical results for the KNITRO software package are presented.

Key Words: nonlinear programming; constrained optimization; sequential quadratic programming; penalty functions; global convergence


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