-

 

 

 




Optimization Online





 

Gradient consistency for integral-convolution smoothing functions

James V. Burke(burke***at***math.washington.edu)
Tim Hoheisel(hoheisel***at***mathematik.uni-wuerzburg.de)
Christian Kanzow(kanzow***at***mathematik.uni-wuerzburg.de)

Abstract: Chen and Mangasarian (1995) developed smoothing approximations to the plus function built on integral-convolution with density functions. X. Chen (2012) has recently picked up this idea constructing a large class of smoothing functions for nonsmooth minimization through composition with smooth mappings. In this paper, we generalize this idea by substituting the plus function for an arbitrary finite max-function. Calculus rules such as inner and outer composition with smooth mappings are provided, showing that the new class of smoothing functions satisfies, under reasonable assumptions, gradient consistency, a fundamental concept coined by Chen (2012). In particular, this guarantees the desired limiting behavior of critical points of the smooth approximations.

Keywords: smoothing method, subdifferential calculus, integral-convolution, piecewise-affine function

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation: Preprint 309, Institute of Mathematics, University of Würzburg, Würzburg, September 2012.

Download: [PDF]

Entry Submitted: 09/08/2012
Entry Accepted: 09/08/2012
Entry Last Modified: 09/08/2012

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society