Comparing different subgradient methods for solving convex optimization problems with functional constraints

Author name not available (Why is that?)

Publication date: 4 January 2021

Abstract: We consider the problem of minimizing a convex, nonsmooth function subject to a closed convex constraint domain. The methods that we propose are reforms of subgradient methods based on Metel--Takeda's paper [Optimization Letters 15.4 (2021): 1491-1504] and Boyd's works [Lecture notes of EE364b, Stanford University, Spring 2013-14, pp. 1-39]. While the former has complexity

m a t h c a l O (v a r e p s i l o n^{- 2 r})

for all

r > 1

, the complexity of the latter is

m a t h c a l O (v a r e p s i l o n^{- 2})

. We perform some comparisons between these two methods using several test examples.

Has companion code repository: https://github.com/dinhthilan/cop

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