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The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion which...

Frictionless contact problem with adhesion for nonlinear elastic materials.

Touzaline, Arezki (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Fritz John's type conditions and associated duality forms in convex non differentiable vector-optimization

I. Kouada (1994)

RAIRO - Operations Research - Recherche Opérationnelle

From Eckart and Young approximation to Moreau envelopes and vice versa

Jean-Baptiste Hiriart-Urruty, Hai Yen Le (2013)

RAIRO - Operations Research - Recherche Opérationnelle

In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.

From first order PDE-systems to harmonic maps between generalized Lagrange spaces.

Neagu, Mircea (2007)

Novi Sad Journal of Mathematics

From optimal control to non-cooperative differential games: a homotopy approach

Alberto Bressan (2009)

Control and Cybernetics

From scalar to vector optimization

Ivan Ginchev, Angelo Guerraggio, Matteo Rocca (2006)

Applications of Mathematics

Initially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem $φ (x) \to min$ , $x \in ℝ^{m}$ , are given. These conditions work with arbitrary functions $φ ℝ^{m} \to \bar{ℝ}$ , but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It...