Results 181 to 190 of about 2,908 (221)

On the subdifferential of a submodular function

Mathematical Programming, 1984
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Dense subdifferentiability and trustworthiness for arbitrary subdifferentials

2010
We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions.
Jules, Florence, Lassonde, Marc
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On Second-Order Subdifferentials and Their Applications

SIAM Journal on Optimization, 2001
We study second-order subdifferentials of nonsmooth functions that are particularly important for applications to sensitivity analysis in optimization and related problems. First we develop various calculus rules for these subdifferentials in rather general settings.
Boris S. Mordukhovich, Jirí V. Outrata
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On the Subdifferentiability of Convex Operators

Journal of the London Mathematical Society, 1986
Let Y be an ordered vector space. Every convex operator ranging in Y admits directional minorant at each point and in every direction of its domain space if and only if every decreasing lower bounded sequence in Y possesses an infimum. This result, combined with a theorem of M. M.
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The Mordukhovich Subdifferentials and Directions of Descent

Journal of Optimization Theory and Applications, 2015
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Pham Duy Khanh, Jen-Chih Yao, Nguyen Dong Yen   +2 more
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Weak Convexity and Approximate Subdifferentials

Journal of Optimization Theory and Applications
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Wim van Ackooij, Felipe Atenas, Claudia A. Sagastizábal   +2 more
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Approximations of Subdifferentials

2014
In practice, the computation of subdifferential is not an easy task. In this chapter, we first consider some families of set-valued mappings that can be used to approximate subdifferentials. Then we define the concept of a discrete gradient that can be used as an approximation of the subgradient at a given point.
Adil Bagirov, Napsu Karmitsa, Marko M. Mäkelä   +2 more
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The properties of the weak subdifferentials

2010
This paper deals with the weak subdifferentials. The properties of the weak subdifferentials are examined. It is showed that the weak subdifferential of a function having a global minimum is not empty.
KASIMBEYLI, Refail, İNCEOĞLU, Gonca
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On σ-Subdifferential Polarity and Fréchet σ-Subdifferential

Numerical Functional Analysis and Optimization, 2023
Mohammad Hossein Alizadeh, Javad Hosseinabadi   +1 more
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Nonlocal Controllability of Sobolev-Type Conformable Fractional Stochastic Evolution Inclusions With Clarke Subdifferential

Bulletin of the Malaysian Mathematical Sciences Society, 2022
Maria Alessandra Ragusa, Hamdy M Ahmed
exaly