Relaxation in Optimization Theory and Variational Calculus

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Walter de Gruyter, 1997 - Mathematics - 474 pages
Introduces applied mathematicians and graduate students to an original relaxation method based on a continuous extension of various optimization problems relating to convex compactification; it can be applied to problems in optimal control theory, the calculus of variations, and non-cooperative game theory. Reviews the background and summarizes the general theory of convex compactifications, then uses it to obtain convex, locally compact envelopes of the Lebesague and Sobolev spaces involved in concrete problems. The nontrivial envelopes cover the classical Young measures as well as various generalizations of them, which can record the limit behavior of fast oscillation and concentration effects. Annotation copyrighted by Book News, Inc., Portland, OR

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Contents

1
1
2
36
Theory of convex compactifications
81
Young measures and their generalizations
102
Convex compactifications of balls in LPspaces
151
Convex σcompactifications of LPspaces
173
Approximation theory
188
Extensions of Nemytskii mappings
202
96
312
Relaxation in variational calculus I
320
3
348
4
366
Relaxation scheme and its FEMapproximation
383
an inner case
391
Relaxation in game theory
412
120
445

Relaxation in optimization theory
222
68
278
4
284

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