Optimization Online


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

Markus Kaiser(markus.kaiser***at***math.uni-wuppertal.de)
Kathrin Klamroth(klamroth***at***math.uni-wuppertal.de)
Alexander Thekale(Alexander.Thekale***at***am.uni-erlangen.de)
Philippe Toint(philippe.toint***at***fundp.ac.be)

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.

Keywords: feasibility problem, nonlinear systems, nonlinear least-squares, structured problems, derivative-free, multidimensional filter, trust-region, global convergence

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: M. Kaiser, K. Klamroth,A. Thekale and Ph. L.Toint, "Solving Structured Nonlinear Least-Squares and Nonlinear Feasibility Problems With Expensive Functions, Technical Report NAXYS-07-2010, University of Namur, Namur, Belgium, 2010.

Download: [PDF]

Entry Submitted: 12/14/2010
Entry Accepted: 12/14/2010
Entry Last Modified: 12/14/2010

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society