All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 104 Next

Displaying 2061 – 2080 of 2377

Showing per page

The distance between subdifferentials in the terms of functions

Libor Veselý (1993)

Commentationes Mathematicae Universitatis Carolinae

For convex continuous functions f , g defined respectively in neighborhoods of points x , y in a normed linear space, a formula for the distance between ∂ f ( x ) and ∂ g ( y ) in terms of f , g (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...

The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

George Isac, George Xian-Zhi Yuan (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...

The Euler-Lagrange inclusion in Orlicz-Sobolev spaces

Hôǹg Thái Nguyêñ, Dariusz Pączka (2014)

Banach Center Publications

We establish the Euler-Lagrange inclusion of a nonsmooth integral functional defined on Orlicz-Sobolev spaces. This result is achieved through variational techniques in nonsmooth analysis and an integral representation formula for the Clarke generalized gradient of locally Lipschitz integral functionals defined on Orlicz spaces.

The interface crack with Coulomb friction between two bonded dissimilar elastic media

Hiromichi Itou, Victor A. Kovtunenko, Atusi Tani (2011)

Applications of Mathematics

We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.

The linear programming approach to deterministic optimal control problems

Daniel Hernández-Hernández, Onésimo Hernández-Lerma, Michael Taksar (1996)

Applicationes Mathematicae

Given a deterministic optimal control problem (OCP) with value function, say J * , we introduce a linear program ( P ) and its dual ( P * ) whose values satisfy sup ( P * ) ≤ inf ( P ) ≤ J * ( t , x ) . Then we give conditions under which (i) there is no duality gap

The linear-quadratic optimal control problem for delay differential equations

Gabriella Di Blasio (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si considera il problema del controllo ottimo per un'equazione lineare con ritardo in uno spazio di Hilbert, con costo quadratico. Si dimostra che il problema della sintesi si traduce in una equazione di Riccati in uno opportuno spazio prodotto e si prova che tale equazione ammette un’unica soluzione.

The Monge problem for strictly convex norms in ℝ d

Thierry Champion, Luigi De Pascale (2010)

Journal of the European Mathematical Society

We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of ℝ d under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.

Currently displaying 2061 – 2080 of 2377