A quasi-second-order proximal bundle algorithm

A quasi-second-order proximal bundle algorithm

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Article ID: iaor19972086
Country: Netherlands
Volume: 73
Issue: 1
Start Page Number: 51
End Page Number: 72
Publication Date: Apr 1996
Journal: Mathematical Programming (Series A)
Authors:
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.

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