Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs

Michael P. Friedlander (mpfcs.ubc.ca)
Sven Leyffer (leyffermcs.anl.gov)

Abstract: We present a two-phase algorithm for solving large-scale quadratic programs (QPs). In the first phase, gradient-projection iterations approximately minimize an augmented Lagrangian function and provide an estimate of the optimal active set. In the second phase, an equality-constrained QP defined by the current inactive variables is approximately minimized in order to generate a second-order search direction. A filter determines the required accuracy of the subproblem solutions and provides an acceptance criterion for the search directions. The resulting algorithm is globally and finitely convergent. The algorithm is suitable for large-scale problems with many degrees of freedom, and provides an alternative to interior-point methods when iterative methods must be used to solve the underlying linear systems. Numerical experiments on a subset of the CUTEr QP test problems demonstrate the effectiveness of the approach.

Keywords: Large-scale optimization, quadratic programming, gradient-projection methods, active-set methods, filter methods, augmented Lagrangian

Category 1: Nonlinear Optimization (Quadratic Programming )

Citation: UBC Department of Computer Science Technical Report TR-2006-18 and Argonne National Laboratory Preprint ANL/MCS-P1370-0906

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Entry Submitted: 09/17/2006
Entry Accepted: 09/17/2006
Entry Last Modified: 06/12/2007

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