Necessary and sufficient conditions for a penalty method to be exact

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Abstract

This paper identifies necessary and sufficient conditions for a penalty method to yield an optimal solution or a Lagrange multiplier of a convex programming problem by means of a single unconstrained minimization. The conditions are given in terms of properties of the objective and constraint functions of the problem as well as the penalty function adopted. It is shown among other things that all linear programs with finite optimal value satisfy such conditions when the penalty function is quadratic.

Original languageEnglish (US)
Pages (from-to)87-99
Number of pages13
JournalMathematical Programming
Volume9
Issue number1
DOIs
StatePublished - Dec 1975
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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