Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems

Eero Tamminen

Research output: Contribution to journalArticle

6 Citations (Scopus)


We consider the following optimization problem: in an abstract set X, find and element x that minimizes a real function f subject to the constraints g(x)≤0 and h(x)=0, where g and h are functions from X into normed vector spaces. Assumptions concerning an overall convex structure for the problem in the image space, the existence of interior points in certain sets, and the normality of the constraints are formulated. A theorem of the alternative is proved for systems of equalities and inequalities, and an intrinsic multiplier rule and a Lagrangian saddle-point theorem (strong duality theorem) are obtained as consequences.
Original languageEnglish
Pages (from-to)93-104
Number of pages12
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1994
MoE publication typeA1 Journal article-refereed


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