University of Illinois Urbana-Champaign

Gaussian Smoothing and Asymptotic Convexity

Mobahi, Hossein; Ma, Yi

Content Files
B40-DC_254.pdf

Permalink

https://hdl.handle.net/2142/74360

Description

Title
Gaussian Smoothing and Asymptotic Convexity
Author(s)
  • Mobahi, Hossein
  • Ma, Yi
Issue Date
2012-03
Keyword(s)
  • Asymptotic convexity
  • Gaussian smoothing
Date of Ingest
  • 2015-04-06T20:54:52Z
  • 2017-07-14T23:14:50Z
Abstract
Smoothing (say by a Guassian kernel) has been a very popular technique for optimizing a nonconvex objective function. The rationale behind smoothing is that the smoothed function has less spurious local minima than the original one. This technique has seen tremendous success in many real world tasks such as those arising in machine learning and computer vision. Despite its empirical success, there has been little theoretical understanding about the effect of smoothing in optimization. This work rigorously studies some of the fundamental properties of the smoothing technique. In particular, we present a formal definition for the functions that can eventually become convex by smoothing. We clarify the related necessary and sufficient conditions and present a closed-form expression for the minimizer of the resulted smoothed function, when it satisfies certain decay conditions.
Publisher
Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report Name or Number
Coordinated Science Laboratory Report no. UILU-ENG-12-2201, DC-254
Type of Resource
text
Genre of Resource
Report (Grant or Annual)
Language
English
Permalink
http://hdl.handle.net/2142/74360
Sponsor(s)/Grant Number(s)
National Science Foundation / NSF IIS 11-16012

Owning Collections

Report - Coordinated Science Laboratory PRIMARY