Using Improved Directions of Negative Curvature for the Solution of Bound-Constrained Nonconvex Problems

Javier Cano (), Javier M. Moguerza () and Francisco J. Prieto ()
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Javier Cano: Rey Juan Carlos University
Javier M. Moguerza: Rey Juan Carlos University
Francisco J. Prieto: Carlos III University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 2, No 7, 474-499

Abstract: Abstract In this work, we describe the efficient use of improved directions of negative curvature for the solution of bound-constrained nonconvex problems. We follow an interior-point framework, in which the key point is the inclusion of computational low-cost procedures to improve directions of negative curvature obtained from a factorisation of the KKT matrix. From a theoretical point of view, it is well known that these directions ensure convergence to second-order KKT points. As a novelty, we consider the convergence rate of the algorithm with exploitation of negative curvature information. Finally, we test the performance of our proposal on both CUTEr/st and simulated problems, showing empirically that the enhanced directions affect positively the practical performance of the procedure.

Keywords: Nonconvex optimisation; Negative curvature; Interior-point methods; KKT conditions; 90C30; 90C51 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1137-9

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