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: | Mifflin Robert |
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.