Relaxation in Optimization Theory and Variational Calculus De Gruyter Nonlinear Analysis and Applications De Gruyter Series in Nonlinear Analysis and Applications 4 2nd Edition by Tomá Roubíek B0B3VWR4QY

Relaxation in Optimization Theory and Variational Calculus De Gruyter Nonlinear Analysis and Applications De Gruyter Series in Nonlinear Analysis and Applications 4 2nd Edition by Tomá Roubíek – Ebook PDF Instant Download/DeliveryISBN:  B0B3VWR4QY 

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ISBN-10 :  B0B3VWR4QY

Author:  Tomá Roubíek 

The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.

Relaxation in Optimization Theory and Variational Calculus De Gruyter Nonlinear Analysis and Applications De Gruyter Series in Nonlinear Analysis and Applications 4 2nd Table of contents:

1 Background generalities
1.1 Order and topology
1.2 Linear and convex analysis
1.3 Optimization theory
1.4 Function and measure spaces
1.5 Means of continuous functions
1.6 Some differential and integral equations
1.7 Non-cooperative game theory
2 Theory of convex compactifications
2.1 Convex compactifications
2.2 Canonical form of convex compactifications
2.3 Convex σ-compactifications
2.4 Approximation of convex compactifications
2.5 Extension of mappings
3 Young measures and their generalizations
3.1 Classical Young measures
3.2 Various generalizations
3.3 Convex compactifications of balls in Lp-spaces
3.4 Convex σ-compactifications of Lp-spaces
3.5 Approximation theory
3.6 Extensions of Nemytskiĭ mappings
4 Relaxation in optimization theory
4.1 Abstract optimization problems
4.2 Optimization problems on Lebesgue spaces
4.3 Example: Optimal control of dynamical systems
4.4 Example: Elliptic optimal control problems
4.5 Example: Parabolic optimal control problems
4.6 Example: Optimal control of integral equations
5 Relaxation in variational calculus I
5.1 Convex compactifications of Sobolev spaces
5.2 Relaxation of variational problems; p > 1
5.3 Optimality conditions for relaxed problems
5.4 Relaxation of variational problems; p= 1
5.5 Convex approximations of relaxed problems
6 Relaxation in variational calculus II
6.1 Prerequisities around quasiconvexity
6.2 Gradient generalized Young functionals
6.3 Relaxation scheme and its FEM-approximation
6.4 Further approximation: an inner case
6.5 Further approximation: an outer case
6.6 Double-well problem: sample calculations
7 Relaxation in game theory
7.1 Abstract game-theoretical problems
7.2 Games on Lebesgue spaces
7.3 Example: Games with dynamical systems
7.4 Example: Elliptic games

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Tags: Relaxation, Optimization, Variational Calculus, Gruyter Nonlinear, Applications, Tomá Roubíek