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Progressive Decoupling of Linkages in Optimization and Variational Inequalities with Elicitable Convexity or Monotonicity

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Abstract

Algorithms for problem decomposition and splitting in optimization and the solving of variational inequalities have largely depended on assumptions of convexity or monotonicity. Here, a way of “eliciting” convexity or monotonicity is developed which can get around that limitation. It supports a procedure called the progressive decoupling algorithm, which is derived from the proximal point algorithm through passing to a partial inverse, localizing and rescaling. In the optimization setting, elicitability of convexity corresponds to a new and very general kind of second-order sufficient condition for a local minimum. Applications are thereby opened up to problem decomposition and splitting even in nonconvex optimization, moreover with augmented Lagrangians for subproblems assisting in the implementation.

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  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    R. Tyrrell Rockafellar

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  1. R. Tyrrell Rockafellar
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Rockafellar, R.T. Progressive Decoupling of Linkages in Optimization and Variational Inequalities with Elicitable Convexity or Monotonicity. Set-Valued Var. Anal 27, 863–893 (2019). https://doi.org/10.1007/s11228-018-0496-1

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  • DOI: https://doi.org/10.1007/s11228-018-0496-1

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