Abstract
This paper presents new versions of proximal bundle methods for solving convex constrained nondifferentiable minimization problems. The methods employϑ 1 orϑ ∞ exact penalty functions with new penalty updates that limit unnecessary penalty growth. In contrast to other methods, some of them are insensitive to problem function scaling. Global convergence of the methods is established, as well as finite termination for polyhedral problems. Some encouraging numerical experience is reported. The ideas presented may also be used in variable metric methods for smooth nonlinear programming.
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This research was supported by the Polish Academy of Sciences.
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Kiwiel, K.C. Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization. Mathematical Programming 52, 285–302 (1991). https://doi.org/10.1007/BF01582892
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DOI: https://doi.org/10.1007/BF01582892
Key words
- Nondifferentiable minimization
- convex programming
- exact penalty functions
- numerical methods
- descent methods
- proximal bundle methods