Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems

R. S. Burachik, Xiaoqi Yang, Y. Y. Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

Using an augmented Lagrangian approach, we study the existence of augmented Lagrange multipliers of a semi-infinite programming problem and discuss their characterizations in terms of saddle points. In the case of a sharp Lagrangian, we obtain a first-order necessary condition for the existence of an augmented Lagrange multiplier for the semi-infinite programming problem and some first-order sufficient conditions by assuming inf-compactness of the data functions and the extended Mangasarian–Fromovitz constraint qualification. Using a valley at 0 augmenting function and assuming suitable second-order sufficient conditions, we obtain the existence of an augmented Lagrange multiplier for the semi-infinite programming problem.
Original languageEnglish
Pages (from-to)471-503
Number of pages33
JournalJournal of Optimization Theory and Applications
Volume173
Issue number2
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • A valley at 0 augmenting function
  • Augmented Lagrange multiplier
  • Optimality conditions
  • Semi-infinite programming
  • Sharp Lagrangian

ASJC Scopus subject areas

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

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