The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization

G. Stephanopoulos, A. W. Westerberg

Research output: Contribution to journalArticle

85 Scopus citations

Abstract

For nonconvex problems, the saddle point equivalence of the Lagrangian approach need not hold. The nonexistence of a saddle point causes the generation of a dual gap at the solution point, and the Lagrangian approach then fails to give the solution to the original problem. Unfortunately, dual gaps are a fairly common phenomenon for engineering system design problems. Methods which are available to resolve the dual gaps destroy the separability of separable systems. The present work employs the method of multipliers by Hestenes to resolve the dual gaps of engineering system design problems; it then develops an algorithmic procedure which preserves the separability characteristics of the system. The theoretical foundations of the proposed algorithm are developed, and examples are provided to clarify the approach taken.

Original languageEnglish (US)
Pages (from-to)285-309
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume15
Issue number3
DOIs
StatePublished - Mar 1 1975
Externally publishedYes

Keywords

  • Decomposition methods
  • duality theory
  • engineering design
  • mathematical programming
  • method of multipliers
  • nonconvex programming

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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