Superlinearly convergent approximate Newton methods for LC1 optimization problems

Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)

Abstract

In the literature, the proof of superlinear convergence of approximate Newton or SQP methods for solving nonlinear programming problems requires twice smoothness of the objective and constraint functions. Sometimes, the second-order derivatives of those functions are required to be Lipschitzian. In this paper, we present approximate Newton or SQP methods for solving nonlinear programming problems whose objective and constraint functions have locally Lipschitzian derivatives, and establish Q-superlinear convergence of these methods under the assumption that these derivatives are semismooth. This assumption is weaker than the second-order differentiability. The extended linear-quadratic programming problem in the fully quadratic case is an example of nonlinear programming problems whose objective functions have semismooth but not smooth derivatives.
Original languageEnglish
Pages (from-to)277-294
Number of pages18
JournalMathematical Programming
Volume64
Issue number3
Publication statusPublished - 11 May 1994
Externally publishedYes

Keywords

  • Iteration
  • Semismoothness
  • Superlinear convergence

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research
  • Software
  • Computer Graphics and Computer-Aided Design
  • Computer Science(all)

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