Dealing with singularities in nonlinear unconstrained optimization

We propose new trust-region based optimization algorithms for solving unconstrained nonlinear problems whose second derivatives matrix is singular at a local solution. We give a theoretical characterization of the singularity in this context and we propose an iterative procedure which allows to identify a singularity in the objective function during the course of the optimization algorithm, and artificially adds curvature to the objective function. Numerical tests are performed on a set of unconstrained nonlinear problems, both singular and non-singular. Results illustrate the significant performance improvement compared to classical trust-region and filter algorithms proposed in the literature.

Published as:
Bierlaire and Thémans, 2009
Bierlaire, M., and Thémans, M. (2009). Dealing with singularities in nonlinear unconstrained optimization, European Journal of Operational Research 196(1):33-42.
ISI 2004: Impact factor: 2.093, cited half-life: 8.3