Optimization Online


Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

Coralia Cartis(coralia.cartis***at***maths.ox.ac.uk)
Nicholas I. M. Gould(nick.gould***at***stfc.ac.uk)
Philippe L. Toint(philippe.toint***at***unamur.be)

Abstract: Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.

Keywords: nonilnear optimization, complexity, optimality conditions

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Nonlinear Optimization (Bound-constrained Optimization )

Category 3: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: naXys, University of Namur, May 2017.

Download: [PDF]

Entry Submitted: 05/20/2017
Entry Accepted: 05/20/2017
Entry Last Modified: 05/20/2017

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 Optimization Society