Citation

BibTex format

@article{Parpas:2016:10.1007/s10957-016-0963-5,
author = {Parpas, P and Rustem and Duy, VN Luong and Rueckert and Parpas, P and Luong and Rustem and Rueckert},
doi = {10.1007/s10957-016-0963-5},
journal = {Journal of Optimization Theory and Applications},
pages = {900--915},
title = {A weighted Mirror Descent algorithm for nonsmooth convex optimization problem},
url = {http://dx.doi.org/10.1007/s10957-016-0963-5},
volume = {170},
year = {2016}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - Large scale nonsmooth convex optimization is a common problemfor a range of computational areas including machine learning and computer vision. Problems in these areas contain special domain structures and characteristics. Special treatment of such problem domains, exploiting their structures, can significantly reduce the computational burden. In this paper, we consider a Mirror Descent method with a special choice of distance function for solving nonsmooth optimization problems over a Cartesian product of convex sets. We propose to use a nonlinear weighted distance in the projectionstep. The convergence analysis identifies optimal weighting parameters that, eventually, lead to the optimally weighted step-size strategy for every projection on a corresponding convex set. We show that the optimality bound of the Mirror Descent algorithm using the weighted distance is either an improvement to, or in the worst-case as good as, the optimality bound of the Mirror Descent using unweighted distances. We demonstrate the efficiency of the algorithm by solving the Markov Random Fields (MRF) optimization problem. In order to exploit the domain of the MRF problem, we use a weighted logentropy distance and a weighted Euclidean distance. Promising experimentalresults demonstrate the effectiveness of the proposed method.
AU - Parpas,P
AU - Rustem
AU - Duy,VN Luong
AU - Rueckert
AU - Parpas,P
AU - Luong
AU - Rustem
AU - Rueckert
DO - 10.1007/s10957-016-0963-5
EP - 915
PY - 2016///
SN - 1573-2878
SP - 900
TI - A weighted Mirror Descent algorithm for nonsmooth convex optimization problem
T2 - Journal of Optimization Theory and Applications
UR - http://dx.doi.org/10.1007/s10957-016-0963-5
UR - http://hdl.handle.net/10044/1/33370
VL - 170
ER -