A quasi-second-order proximal bundle algorithm |
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Authors: | Robert Mifflin |
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Institution: | (1) Department of Pure and Applied Mathematics, Washington State University, 99164-3113 Pullman, WA, USA |
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Abstract: | This paper introduces an algorithm for convex minimization which includes quasi-Newton updates within a proximal point algorithm
that depends on a preconditioned bundle subalgorithm. The method uses the Hessian of a certain outer function which depends
on the Jacobian of a proximal point mapping which, in turn, depends on the preconditioner matrix and on a Lagrangian Hessian
relative to a certain tangent space. Convergence is proved under boundedness assumptions on the preconditioner sequence.
Research supported by NSF Grant No. DMS-9402018 and by Institut National de Recherche en Informatique et en Automatique, France. |
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Keywords: | Bundle methods Convex minimization Global convergence Proximal point Quasi-Newton Variable metric algorithms |
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