Optimality Functions and Lopsided Convergence

Abstract

Optimality functions pioneered by E. Polak characterize stationary points, quantify the degree with which a point fails to be stationary, and play central roles in algorithm development. For optimization problems requiring approximations, optimality functions can be used to ensure consistency in approximations, with the consequence that optimal and stationary points of the approximate problems indeed are approximately optimal and stationary for an original problem. In this paper, we review the framework and apply it to nonlinear programming. This results in a convergence result for a primal interior point method without constraint qualifications or convexity assumptions. Moreover we introduce lopsided convergence of bifunctions on metric spaces and show that this notion of convergence is instrumental in establishing consistency of approximations. Lopsided convergence also leads to further characterizations of stationary points under perturbations and approximations.

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Document Details

Document Type
Technical Report
Publication Date
Mar 16, 2015
Accession Number
ADA625028

Entities

People

  • Johannes Ø. Røyset
  • Roger J-B Wets

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Consistency
  • Construction
  • Convergence
  • Convex Sets
  • Differential Equations
  • Evolutionary Algorithms
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Nonlinear Programming
  • Operations Research
  • Optimization
  • Qualifications
  • Sequences
  • Theorems

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research
  • Systems Analysis and Design

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers