ON THE EVALUATION COMPLEXITY OF CUBIC REGULARIZATION METHODS FOR POTENTIALLY RANK-DEFICIENT NONLINEAR LEAST-SQUARES PROBLEMS AND ITS RELEVANCE TO CONSTRAINED NONLINEAR OPTIMIZATION

Coralia Cartis*, Nicholas I. M. Gould, Philippe L. Toint

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a new termination criterion suitable for potentially singular, zero or nonzero residual, least-squares problems, with which cubic regularization variants take at most O(epsilon(-3/2)) residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below epsilon; this is the best known bound for potentially rank-deficient nonlinear least-squares problems. We then apply the new optimality measure and cubic regularization steps to a family of least-squares merit functions in the context of a target-following algorithm for nonlinear equality-constrained problems; this approach yields the first evaluation complexity bound of order epsilon(-3/2) for nonconvexly constrained problems when higher accuracy is required for primal feasibility than for dual first-order criticality.

Original languageEnglish
Pages (from-to)1553-1574
Number of pages22
JournalSiam journal on optimization
Volume23
Issue number3
DOIs
Publication statusPublished - 2013

Keywords

  • evaluation complexity
  • worst-case analysis
  • least-squares problems
  • constrained nonlinear optimization
  • cubic regularization methods
  • TRUST REGION ALGORITHM
  • UNCONSTRAINED OPTIMIZATION
  • GLOBAL PERFORMANCE
  • PENALTY-FUNCTION
  • NEWTON METHODS
  • MINIMIZATION
  • CONVERGENCE

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