A Limited-Memory Quasi-Newton Algorithm for Bound-Constrained Nonsmooth Optimization

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search. The key ingred...

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Veröffentlicht in:arXiv.org
Hauptverfasser: Keskar, Nitish Shirish, Waechter, Andreas
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 21.12.2016
Schlagworte:
Algorithms
Approximation
Continuity (mathematics)
Curvature
Iterative methods
Mathematical analysis
Nonlinear programming
Optimization
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ISSN:2331-8422
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Zusammenfassung:We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that defines the subspace in which search directions are computed. To overcome the inherent shortsightedness of the gradient for a nonsmooth function, we propose two strategies. The first relies on an approximation of the \(\epsilon\)-minimum norm subgradient, and the second uses an iterative corrective loop that augments the active set based on the resulting search directions. We describe a Python implementation of the proposed algorithm and present numerical results on a set of standard test problems to illustrate the efficacy of our approach.
Bibliographie:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422