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Sequential quadratic programming methods. (English) Zbl 1242.90297

Lee, Jon (ed.) et al., Mixed integer nonlinear programming. Selected papers based on the presentations at the IMA workshop mixed-integer nonlinear optimization: Algorithmic advances and applications, Minneapolis, MN, USA, November 17–21, 2008. New York, NY: Springer (ISBN 978-1-4614-1926-6/hbk; 978-1-4614-1927-3/ebook). The IMA Volumes in Mathematics and its Applications 154, 147-224 (2012).
Summary: 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
For the entire collection see [Zbl 1230.90005].

MSC:

90C55 Methods of successive quadratic programming type
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
49J20 Existence theories for optimal control problems involving partial differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M37 Numerical methods based on nonlinear programming
65F05 Direct numerical methods for linear systems and matrix inversion
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Software:

MA57; QPA; MISQP
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