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On the Performance of SQP Methods for Nonlinear Optimization

Philip Gill (pgill***at***ucsd.edu)
Michael Saunders (saunders***at***stanford.edu)
Elizabeth Wong (elwong***at***ucsd.edu)

Abstract: This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are given for more than 1150 problems from the CUTEst test collection. The results indicate that SQP methods based on maintaining a quasi-Newton approximation to the Hessian of the Lagrangian function are both reliable and efficient for general large-scale optimization problems. In particular, the results show that in some situations, quasi-Newton methods are more efficient than competing methods based on using the exact Hessian of the Lagrangian. The paper concludes with the discussion of an SQP method that employs both approximate and exact Hessian information. In this approach the quadratic programming subproblem is either the conventional subproblem defined in terms of a positive-definite quasi-Newton approximate Hessian, or a convexified problem based on the exact Hessian.

Keywords: Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, second-derivative methods

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Optimization Software and Modeling Systems (Optimization Software Benchmark )

Citation: UCSD Center for Computational Mathematics, Technical Report 15-1, January 2015

Download: [PDF]

Entry Submitted: 01/31/2015
Entry Accepted: 01/31/2015
Entry Last Modified: 02/06/2015

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