Results 141 to 150 of about 508 (181)

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
The authors study second-order subdifferentials of extended-real-valued functions. The starting point is the second-order subdifferential introduced by the first author as the coderivative of the first-order subdifferentiable mapping. Beside this, a semiconvex version is introduced as the coderivative of the convexified first-order subdifferential ...
Boris S. Mordukhovich, Jirí V. Outrata
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Hunting for a Smaller Convex Subdifferential

Journal of Global Optimization, 1997
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Vladimir F. Demyanov, Vaithilingam Jeyakumar   +1 more
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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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Infinitesimals and Subdifferentials

2002
The nonstandard methods of analysis have been applied to various fields of mathematics. In the present chapter we shall consider the use of infinitesimals in subdifferential calculus, one of the new branches of functional analysis which originated from evolution of the theory of extremal problems.
E. I. Gordon, A. G. Kusraev, S. S. Kutateladze   +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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Conjugates and Subdifferentials

2014
To each type of efficiency for optimization problems it is possible to associate notions of conjugate and subdifferential for vector valued functions or set-valued maps. In this chapter we study the conjugate and the subdifferential corresponding to the strong efficiency as well as the subdifferentials corresponding to the weak and Henig type ...
Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu   +2 more
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