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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Administrative Contact:
Terry Le

Office: AP&M 7431
Phone: (858)534-9813
Fax: (858)534-5273
E-mail: tele@ucsd.edu
Second-Derivative SQP Methods

Vyacheslav Kungurtsev
UCSD

Abstract:

Sequential Quadratic Programming (SQP) methods are a popular and successful class of methods for minimizing a generally nonlinear function subject to nonlinear constraints. Under a standard set of assumptions, conventional SQP methods exhibit a fast local convergence rate. However, in practice, a conventional SQP method involves solving an indefinite quadratic program (QP), which is NP hard. As a result, approximations to the second-derivatives are often used, slowing the local convergence rate and reducing the chance that the algorithm will converge to a local minimizer instead of a saddle point. In addition, the standard assumptions required for convergence often do not hold in practice. For such problems, regularized SQP methods, which also require second-derivatives, have been shown to have good local convergence properties; however, there are few regularized SQP methods that exhibit convergence to a minimizer from an arbitrary initial starting point. My thesis considers the formulation, analysis and implementation of: (i) practical methods that use exact second-derivative information but do not require the solution of an indefinite QP, (i) a regularized SQP method with global convergence and (iii) a rigorously defined version of a conventional SQP method with features that have been observed to work in practice for degenerate problems.

Tuesday, April 17, 2012
11:00AM AP&M 2402