Comparing different subgradient methods for solving convex optimization problems with functional constraints
This work provides incremental insights for researchers in optimization by comparing existing methods on standard test problems.
The paper tackles the problem of minimizing convex, nonsmooth functions with constraints by comparing two subgradient methods, one with complexity O(ε^{-2r}) for r>1 and the other with O(ε^{-2}), using test examples to evaluate their performance.
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 $\mathcal{O}(\varepsilon^{-2r})$ for all $r> 1$, the complexity of the latter is $\mathcal{O}(\varepsilon^{-2})$. We perform some comparisons between these two methods using several test examples.