Composition and union of general algorithms of optimization

The study of the convergence of algorithms of optimization obtained by composition or union, taken in sense of the relaxation, is done. After having recalled the Zangwill’s theorem and given two extensions we study the obtainment of generalized fixed points in the framework of the composition or the union of algorithms obtained in a free steering way for, firstly functions having a unique maximum over some particular subsets, ranges of the current point, and secondly for general functions. The validity of the different hypotheses is discussed through some examples.

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