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A second derivative SQP method: theoretical issues

Nick I. M. Gould (nick.gould***at***stfc.ac.uk)
Daniel P. Robinson (daniel.p.robinson***at***gmail.com)

Abstract: Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second-derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which ``guides'' the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established.

Keywords: Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, $\ell_1$ penalty function, nonsmooth optimization

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: University of Oxford, Numerical Analysis Group and Rutherford Appleton Laboratory

Download: [PDF]

Entry Submitted: 10/31/2008
Entry Accepted: 10/31/2008
Entry Last Modified: 11/11/2008

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