Proximal subgradient method for non-Lipschitz objective functions.
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| Title: | Proximal subgradient method for non-Lipschitz objective functions. |
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| Authors: | Toyoda, Mitsuru1 (AUTHOR) toyoda@tmu.ac.jp, Tanaka, Mirai2,3 (AUTHOR) |
| Source: | Optimization Methods & Software. Aug2025, Vol. 40 Issue 4, p755-782. 28p. |
| Subjects: | Subgradient methods, Mathematical optimization, Lipschitz continuity, Empirical research, Asymptotic analysis, Convex functions, Optimization algorithms |
| Abstract: | This paper presents a convergence analysis framework of the proximal subgradient method for optimization problems involving non-Lipschitz continuous objective functions. In the conventional analysis of the various subgradient methods, including the proximal subgradient method, the Lipschitz continuity assumption has been placed to guarantee the boundedness of the subgradient and derive the convergence rate. However, the Lipschitz continuity does not hold in practical problems, including the sum-of- $ \ell _2 $ ℓ 2 -norms (SO $ \ell _2 $ ℓ 2 N) optimal control problem, which is examined in the numerical experiments of this paper. Without the Lipschitz continuity assumption, this paper provides the convergence analysis for strongly convex and non-strongly convex objective functions under mild assumptions. Suitable stepsize rules and resulting convergence rates are established; non-strongly convex cases result in a rate close to the rate of the existing subgradient method, and strongly convex cases achieve the same rate as the existing convergence analysis. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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