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

publication date

  • August 2017

start page

  • 474

end page

  • 499


  • 2


  • 174

International Standard Serial Number (ISSN)

  • 0022-3239

Electronic International Standard Serial Number (EISSN)

  • 1573-2878


  • 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.


  • nonconvex optimisation; negative curvature; interior-point methods; kkt conditions