A trust-region method for constrained derivative-free optimization and worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization.

Student thesis: Doc typesDoctor of Sciences

Abstract

This work is divided into two parts related to two research topics that have received increasing attention of the optimization community over the past years. The first part is concerned with the design and implementation of a new trust-region method for constrained derivative-free optimization. This method is based on interpolation models and employs a self-correcting geometry procedure in order to ensure that the geometry of the interpolation set does not differ too much from the ideal one. Numerical results of the proposed method are also presented. The second part analyzes the worst-case evaluation complexity of the class of non-monotone gradient-related algorithms for smooth nonconvex and unconstrained problems. We show that this class of methods requires at most O(ε-2) function evaluations to find a point with the gradient norm below a threshold ε > 0.
Date of Award25 Aug 2015
Original languageEnglish
Awarding Institution
  • University of Namur
SponsorsUniversité de Namur & CERUNA
SupervisorPhilippe Toint (Supervisor), Anne Lemaitre (President), Annick Sartenaer (Jury), Andrew Conn (Jury) & Serge Gratton (Jury)

Keywords

  • numerical optimization
  • derivative-free optimization
  • black-box optimization
  • nonlinear constrained optimization
  • trust-region methods
  • nonconvex unconstrained optimization
  • evaluation complexity
  • nonmonotone linesearch algorithms

Cite this

A trust-region method for constrained derivative-free optimization and worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization.
Rodrigues Sampaio, P. (Author). 25 Aug 2015

Student thesis: Doc typesDoctor of Sciences