A Second Derivative SQP Method: Global Convergence

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. Key words. Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, ℓ1-penalty function, nonsmooth ...

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Nicholas I. M. Gould, Daniel P. Robinson
• Keywords: Quadratic Programming, Sequential Quadratic Programming, SIAMJO 2010, Sqp Method