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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.

    Note:

    Published as: Dealing with singularities in nonlinear unconstrained optimization, European Journal of Operational Research. 196 (1):33-42 (2009).

    Reference

    • TRANSP-OR-REPORT-2006-018

    Record created on 2008-02-15, modified on 2016-09-16

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