PENALTY METHODS FOR MATHEMATICAL PROGRAMMING IN E(n) WITH GENERAL CONSTRAINT SETS.

Abstract

This paper extends the principal supporting results and the general convergence theorems for penalty methods, obtained by Fiacco and McCormick 'Nonlinear Programming: Sequential Unconstrained Minimization Techniques (1968)' for the continuous mathematical programming problem, to the problem of minimizing a mildly regulated objective function over any nonempty subset of E to the n th power. The constraint set need not be defined and the desired minimizing sequence is shown to exist, without additional assumptions (i.e., other than those invoked in the principal convergence theorem of nonlinear programming). A particularly interesting consequence is the fact that a discrete (e.g., integer) programming problem can be solved by a single unconstrained minimization of the auxiliary function. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1969
Accession Number
AD0695660

Entities

People

  • Anthony V. Fiacco

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programming
  • Convergence
  • Interdisciplinary Science
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Systems Analysis and Design