Relaxation in Optimization Theory and Variational Calculus

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F20%3A00536072" target="_blank" >RIV/61388998:_____/20:00536072 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.degruyter.com/view/title/537021" target="_blank" >https://www.degruyter.com/view/title/537021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/9783110590852" target="_blank" >10.1515/9783110590852</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relaxation in Optimization Theory and Variational Calculus

Popis výsledku v původním jazyce

In this monograph, relaxation means an extension of optimization or variational problems in a certain natural way, typically by some continuity. Beside compactness, also convexity is the main attribute of the extended (so-called relaxed) problems,which yields existence and stability of their solutions as well as optimality conditions, or allows for using some fixed-point theorems, especially in noncooperative game theory. The book offers an exposition of an original abstract theory of convex compactifications and of application to various concrete problems in optimal control and calculus of variations. Classical Young measures and their numerous generalizations are used to capture various fast oscillation and possibly concentration phenomena in the limits. In particular, one can construct convex locally compact metrizable envelopes of Lebesgue spaces, typically occuring in original (nonrelaxed) problems and here embedded densely into such envelopes. Also numerical aspects are pursued. This new edition reflects in particular also the achievements within quarter a century that passed from the first edition. Many improvements of the presentation and expansions have been added, too.

Název v anglickém jazyce

Relaxation in Optimization Theory and Variational Calculus

Popis výsledku anglicky

In this monograph, relaxation means an extension of optimization or variational problems in a certain natural way, typically by some continuity. Beside compactness, also convexity is the main attribute of the extended (so-called relaxed) problems,which yields existence and stability of their solutions as well as optimality conditions, or allows for using some fixed-point theorems, especially in noncooperative game theory. The book offers an exposition of an original abstract theory of convex compactifications and of application to various concrete problems in optimal control and calculus of variations. Classical Young measures and their numerous generalizations are used to capture various fast oscillation and possibly concentration phenomena in the limits. In particular, one can construct convex locally compact metrizable envelopes of Lebesgue spaces, typically occuring in original (nonrelaxed) problems and here embedded densely into such envelopes. Also numerical aspects are pursued. This new edition reflects in particular also the achievements within quarter a century that passed from the first edition. Many improvements of the presentation and expansions have been added, too.

Druh

B - Odborná kniha

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA19-04956S" target="_blank" >GA19-04956S: Dynamika a nelineární chování pokročilých kompozitních struktur; modelování a optimalizace</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-3-11-058962-7

Počet stran knihy

474

Název nakladatele

Walter de Gruyter

Místo vydání

Berlin

Kód UT WoS knihy

—