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

作者：Cano Javier^*; Moguerza Javier M; Prieto Francisco J

来源：Journal of Optimization Theory and Applications, 2017, 174(2): 474-499.

DOI：10.1007/s10957-017-1137-9

• Nonconvex optimisation
• Negative curvature
• Interior-point methods
• KKT conditions

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.

• 出版日期2017-8