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Comparing different subgradient methods for solving convex optimization problems with functional constraints
Thi Lan Dinh, Ngoc Hoang Anh Mai
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 𝒪(ε⁻²ʳ) for all r> 1, the complexity of the latter is 𝒪(ε⁻²). We perform some comparisons between these two methods using several test examples.
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