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Sequential Quadratic Programming Methods

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Mixed Integer Nonlinear Programming

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 154))

Abstract

In his 1963 PhD thesis, Wilson proposed the first sequential quadratic programming (SQP) method for the solution of constrained nonlinear optimization problems. In the intervening 48 years, SQP methods have evolved into a powerful and effective class of methods for a wide range of optimization problems. We review some of the most prominent developments in SQP methods since 1963 and discuss the relationship of SQP methods to other popular methods, including augmented Lagrangian methods and interior methods. Given the scope and utility of nonlinear optimization, it is not surprising that SQP methods are still a subject of active research. Recent developments in methods for mixed integer nonlinear programming (MINLP) and the minimization of functions subject to differential equation constraints has led to a heightened interest in methods that may be “warm started” from a good approximate solution. We discuss the role of SQP methods in these contexts

AMS(MOS) subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-0915220, and the Department of Energy under grant DE-SC0002349.

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  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Philip E. Gill & Elizabeth Wong

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    Jon Lee

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    Sven Leyffer

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Gill, P.E., Wong, E. (2012). Sequential Quadratic Programming Methods. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1927-3_6

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