Journal
MATHEMATICAL PROGRAMMING
Volume 122, Issue 2, Pages 273-299Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-008-0248-3
Keywords
Large-scale optimization; Constrained optimization; Nonconvex programming; Inexact linear system solvers; Krylov subspace methods
Categories
Funding
- National Science Foundation [CCR-0219190, CHE-0205170, CCF-0514772]
- Department of Energy [DE-FG02-87ER25047-A004]
- Intel Corporation
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We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351-369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.
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