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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

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