Results 141 to 150 of about 3,697 (188)

Approximative quasi-subdifferentials

Optimization, 2007
We introduce a kind of approximative quasi-subdifferential useful for the characterization of quasi-convex, lower semicontinuous functions. The relationship existing between this notion and some quasi-subdifferentials known in the literature is studied.
T. Precupanu, C. Stamate
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Subdifferentiability and Inf-Sup Theorems

Positivity, 1999
The authors present an abstract set of hypotheses yielding the equality \[ \underset{y\in Y}{\text{Sup}} \underset{x\in X} {\text{Inf}} L(x,y)= \underset{x\in X} {\text{Inf}} \underset{y\in Y} {\text{Sup}} L(x,y), \] where \(L\) is an extended-real-valued function defined on the Cartesian product \(X\times Y\).
Moussaoui, Mohammed, Volle, Michel
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Subdifferentiability and the Duality Gap

Positivity, 2002
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Gretsky, N. E., Ostroy, J. M., Zame, W. R.   +2 more
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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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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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Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey

Nonlinear Analysis: Theory, Methods & Applications, 1995
The aim of this survey paper is to present calculus rules for the subdifferential \(\partial f\) of a convex function \(f\) constructed from other convex functions \(f_i\) by means of the main operations encountered in convex analysis, without any qualification conditions.
Hiriart-Urruty, J.-B., Moussaoui, M., Seeger, A., Volle, M.   +3 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 Sagastizábal   +2 more
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Variational Subdifferential for Quasiconvex Functions

Journal of Optimization Theory and Applications, 2001
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Subdifferentials with Autoconjugate Fitzpatrick Function

Set-Valued and Variational Analysis, 2011
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Das konvexe Subdifferential

2021
Das zentrale Werkzeug zur konkreten Umsetzung des Satzes von Lewis und Pang ist das Subdifferential einer konvexen Funktion, das das vorliegende Kapitel ausfuhrlich diskutiert. Wir sehen unter anderem, wie sich die einseitige Richtungsableitung einer konvexen Funktion und ihr Subdifferential wechselseitig auseinander konstruieren lassen, und dass sich ...
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