Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials
Knossalla M (2018)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2018
Journal
Pages Range: 1-21
DOI: 10.1080/02331934.2018.1426579
Abstract
Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the
objective function.
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How to cite
APA:
Knossalla, M. (2018). Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials. Optimization, 1-21. https://dx.doi.org/10.1080/02331934.2018.1426579
MLA:
Knossalla, Martin. "Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials." Optimization (2018): 1-21.
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