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Finite-tight sets

Liviu Florescu (2007)

Open Mathematics

We introduce two notions of tightness for a set of measurable functions - the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of...

First Order Characterizations of Pseudoconvex Functions

Ivanov, Vsevolod (2001)

Serdica Mathematical Journal

First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

Ginchev, Ivan, Ivanov, Vsevolod I. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...

Fractional Roesser problem and its optimization

Rafał Kamocki (2014)

Banach Center Publications

In the paper, a fractional continuous Roesser model is considered. Existence and uniqueness of a solution and continuous dependence of solutions on controls of the nonlinear model are investigated. Next, a theorem on the existence of an optimal solution for linear model with variable coefficients is proved.

Frictionless contact problem with adhesion and finite penetration for elastic materials

Arezki Touzaline (2010)

Annales Polonici Mathematici

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...

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