A Second Derivative SQP Method: Global Convergence

  • Authors:
  • Nicholas I. M. Gould;Daniel P. Robinson

  • Affiliations:
  • nick.gould@stfc.ac.uk;robinson@maths.ox.ac.uk

  • Venue:
  • SIAM Journal on Optimization
  • Year:
  • 2010

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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.