MATHEMATICAL PROGRAMMING

Abstract

Our objective is to provide a more general theoretical basis for those methods for solving constrained minimization problems that are based on successive unconstrained minimizations of a parametric auxiliary function. In order to do this, we first give basic defining properties of a general auxiliary function and obtain a proof of local convergence for the mildly regulated nonconvex problem. We proceed from this general result to develop a family of auxiliary functions by giving the general function more and more structure, eventually being led to the general form of the 'penalty' functions that conventionally have been utilized. Similarly, the problem structure is increasingly specialized and we deal finally with the convex problem. As expected, stronger results are obtained as additional structure is assumed.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0656904

Entities

People

  • Anthony V. Fiacco

Organizations

  • Northwestern University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Computer Programming
  • Continuity
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  • Contracts
  • Convergence
  • Convex Programming
  • Instructions
  • Mathematical Programming
  • Military Research
  • Nonlinear Programming
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Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Systems Analysis and Design