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1
Content available remote Unilateral contact applications using FEM software
100%
Stavroulaki M. E. , Stavroulakis G. E.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 1
115-125
EN
Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly presented, together with elements of the underlying theory.
2
Content available remote A note on strong pseudoconvexity
88%
Ivanov V.
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tom 6
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nr 4
576-580
EN
A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
3
An intersection formula for the normal cone associated with the hypertangent cone
75%
Ciligot-Travain M.
Journal of Applied Analysis
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1999
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tom Vol. 5, nr 2
239-247
EN
The aim of this work is to present a new result about estimation of the hypertangent normal cone of an intersection without using directionally Lipschitz assumptions.
4
Content available remote A short proof of the separable reduction theorem
75%
Penot J. P.
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2010
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tom Vol. 43, nr 3
653-663
EN
We present a simple proof of the separable reduction theorem, a crucial result of nonsmooth analysis which allows to extend to Asplund spaces the results known for separable spaces dealing with Fréchet subdifferentials. It relies on elementary results in convex analysis and avoids certain technicalities.
5
Content available remote Unilateral Contact Applications Using Fem Software
75%
Stavroulaki M. E. , Stavroulakis G. E.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom Vol. 12, no 1
115-125
EN
Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly presented, together with elements of the underlying theory.
6
Second-order characterizations of convex and pseudoconvex functions
75%
Ginchev I. , Ivanov V. I.
Journal of Applied Analysis
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2003
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tom Vol. 9, nr 2
261-273
EN
The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions f: X —> R defined on a convex subset X of a real linear space E in terms of first and second-order upper Dini-directional derivatives. Observing that the property f radially u.s.c. does not require a topological structure of E, we draw the possibility to state our results for arbitrary real linear spaces. For convex functions we extend a theorem of Huang, Ng [10]. For pseudoconvex functions we generalize results of Diewert, Avriel, Zang [6] and Crouzeix [4]. While some known results on pseudoconvex functions are stated in global concepts (e.g. Komlosi [11]), we succeeded in realizing the task to confine to local concepts only.
7
On strict pseudoconvexity
75%
Ivanov V. I.
Journal of Applied Analysis
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2007
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tom Vol. 13, nr 2
183-196
EN
The present paper provides first and second-order characterizations of a radilly lower semicontinuous strictly pseudoconvex function ∫ : X → R defined on a convex set X in the real Euclidean space Rn in twerms of the lower Dini-directional derivative. In particular we obtain connections between the strictly pseudoconvex functions, nonlinear programming problem, Stampacchia variational inequality, and strict Minty variational inequality. We extend to the radially continuous functions the characterization due to Diewert, Avriel, Zang [6]. A new implication appears in our conditions. Connections with other classes of functions are also derived
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