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A Framework for Reduce-or-Retreat Minimization

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Stationarity and Convergence in Reduce-or-Retreat Minimization

Part of the book series: SpringerBriefs in Optimization ((BRIEFSOPTI))

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Abstract

We introduce our framework, including all of the elements generated at each iteration, as well as the major components of reduction and retreat. The property of nonincreasing function values inherent in the framework is strengthened via the definition of a descent method, and lower-diminishing target-gaps are explored as the result of a successful run of a method within the framework. Finally, we develop our extended notion of approaching stationarity and link this property both to stationary points and to lower-diminishing target-gaps.

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Authors and Affiliations

  1. Department of Mathematics, Bowdoin College, Brunswick, ME, USA

    Adam B. Levy

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  1. Adam B. Levy
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© 2012 Adam B. Levy

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Levy, A.B. (2012). A Framework for Reduce-or-Retreat Minimization. In: Stationarity and Convergence in Reduce-or-Retreat Minimization. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4642-2_1

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