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: Dealing with singularities in nonlinear unconstrained optimization, European Journal of Operational Research. 196 (1):33-42 (2009).
Record created on 2008-02-15, modified on 2017-02-16