The Mathematical Institute, University of Oxford, Eprints Archive

A second derivative SQP method: theoretical issues

Gould, Nicholas I. M. and Robinson, Daniel P. (2008) A second derivative SQP method: theoretical issues. Technical Report. SIAM Journal on Optimization. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Operations research, mathematical programming
A - C > Calculus of variations and optimal control
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:873
Deposited By:Lotti Ekert
Deposited On:17 Dec 2009 08:04
Last Modified:17 Dec 2009 08:04

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