SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

Abstract. Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse. Second derivatives are assumed to be unavailable or too expensive to calculate. We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. The Hessian of the Lagrangian is approximated using a limited-memory quasi-Newton method. SNOPT is a particular implementation that uses a reduced-Hessian semidefinite QP solver (SQOPT) for the QP subproblems. It is designed for problems with many thousands of constraints and variables but is best suited for problems with a moderate number of degrees of freedom (...

• Type: Journal
• Year: 2002
• Where: SIAMJO
• Authors: Philip E. Gill, Walter Murray, Michael A. Saunders
• Keywords: Nonlinear, QP Subproblems, Sequential Quadratic Programming, SIAMJO 2002