SNOPT: an SQP algorithm for large-scale constrained optimization. (English) Zbl 1210.90176

Summary: 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 (say, up to 2000). Numerical results are given for most of the CUTEr and COPS test collections (about 1020 examples of all sizes up to 40000 constraints and variables, and up to 20000 degrees of freedom).


90C55 Methods of successive quadratic programming type
49J20 Existence theories for optimal control problems involving partial differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M37 Numerical methods based on nonlinear programming
65F05 Direct numerical methods for linear systems and matrix inversion
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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