Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

Markus Kaiser, Kathrin Klamroth, Alexander Thekale, Philippe Toint

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Abstract

We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and to obtain a robust method. Under adequate assumptions, we show global convergence to a feasible point. Numerical results indicate a significant reduction in function evaluations compared to other derivative based and derivative-free solvers for nonlinear feasibility problems.
Original languageEnglish
Place of PublicationNamur
PublisherFUNDP. Namur center for complex systems
Volume10(7)
Publication statusPublished - 2010

Publication series

NameNAXYS Technical Report
PublisherDepartment of Mathematics, University of Namur
Volume07-2010

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Keywords

  • derivative-free
  • feasibility problem
  • structured problems
  • global convergence.
  • trust-region
  • nonlinear least-squares
  • nonlinear systems
  • multidimensional filter

Cite this

Kaiser, M., Klamroth, K., Thekale, A., & Toint, P. (2010). Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. (NAXYS Technical Report; Vol. 07-2010). FUNDP. Namur center for complex systems.