"Relative-Continuity" for Non-Lipschitz Non-Smooth Convex Optimization using Stochastic (or Deterministic) Mirror Descent

A. S. Nemirovsky and D. B. Yudin, Problem complexity and method efficiency in optimization , Wiley, New York, 1983

1983

Earlier work this paper cites.

D. Bertsekas, Nonlinear programming , Athena Scientific, Belmont, MA, 1999

1999

Earlier work this paper cites.

A. Beck and M. Teboulle, Mirror descent and nonlinear projected subgradient methods for convex optimization , Operations Research Letters 31

2003

Earlier work this paper cites.

Y. Nesterov, Introductory lectures on convex optimization: a basic course , Kluwer Academic Publishers, Boston, 2003

2003

Earlier work this paper cites.

S. Shalev-Shwartz, Y. Singer, and N. Srebro, Pegasos: Primal estimated sub-gradient solver for SVM , Proceedings of the 24th International Conference on Machine learning, ACM, 2007, pp. 807–814

2007

Earlier work this paper cites.

P. Tseng, On accelerated proximal gradient methods for convex-concave optimization , Tech. report, May 21, 2008

2008

Earlier work this paper cites.

J. Duchi and Y. Singer, Efficient online and batch learning using forward backward splitting , Journal of Machine Learning Research 10

2009

Cited alongside, same era.

J. Yu, S.V.N. Vishwanathan, S. Günter, and N.N. Schraudolph, A quasi-Newton approach to nonsmooth convex optimization problems in machine learning , Journal of Machine Learning Research 11

2010

Cited alongside, same era.

S. Lacoste-Julien, M. Schmidt, and F. Bach, A simpler approach to obtaining an O ⁡ ( 1 / t ) {O}(1/t) convergence rate for the projected stochastic subgradient method , arXiv preprint arXiv:1212.2002 (2012)

Original

2012

Cited alongside, same era.

A. Nedić and S. Lee, On stochastic subgradient mirror-descent algorithm with weighted averaging , SIAM Journal on Optimization 24

2014

Cited alongside, same era.

S. Bubeck, Convex optimization: Algorithms and complexity , Foundations and Trends® in Machine Learning 8

H.H. Bauschke, J. Bolte, and M. Teboulle, A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications , Mathematics of Operations Research 42

2016

Later among the works it cites.

Y. Zhou, Y. Liang, and L. Shen, A unified approach to proximal algorithms using Bregman distance , Tech. report, 2016

Original

2016

Later among the works it cites.

F. Hanzely and P. Richtarik, Randomized methods for minimizing relatively smooth functions , Tech. report, 2017

2017

Closest in time.

Q. Van Nguyen, Forward-backward splitting with Bregman distances , Vietnam Journal of Mathematics 45

2017

Closest in time.

H. Lu, R. M. Freund, and Y. Nesterov, Relatively smooth convex optimization by first-order methods, and applications , SIAM Journal on Optimization 28

2018