- A second derivative SQP method: theoretical issues Nick I. M. Gould (nick.gouldstfc.ac.uk) Daniel P. Robinson (daniel.p.robinsongmail.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: 10/31/2008Entry Accepted: 10/31/2008Entry Last Modified: 11/11/2008Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.