On iterated minimization in nonconvex optimization

H.Th. Jongen, T. Möbert, K. Tammer

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In dynamic programming and decomposition methods one often applies an iterated minimization procedure. The problem variables are partitioned into several blocks, say x and y. Treating y as a parameter, the first phase consists of minimization with respect to the variable x. In a second phase the minimization of the resulting optimal value function depending on y is considered. In this paper we treat this basic idea on a local level. It turns out that strong stability (in the sense of Kojima) in the first phase is a natural assumption. In order to show that the iterated local minima of the parametric problem lead to a local minimum for the whole problem, we use a generalized version of a positive definiteness criterion of Fujiwara-Han-Mangasarian.
Original languageUndefined
Pages (from-to)679-691
JournalMathematics of operations research
Issue number4
Publication statusPublished - 1986


  • IR-98548

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