By Jean-Baptiste Hiriart-Urruty, Adam Korytowski, Helmut Maurer, Maciej Szymkat

ISBN-10: 3319307843

ISBN-13: 9783319307848

ISBN-10: 3319307851

ISBN-13: 9783319307855

This ebook comprises prolonged, in-depth shows of the plenary talks from the sixteenth French-German-Polish convention on Optimization, held in Kraków, Poland in 2013. each one bankruptcy during this ebook shows a entire examine new theoretical and/or application-oriented ends up in mathematical modeling, optimization, and optimum keep watch over. scholars and researchers eager about photograph processing, partial differential inclusions, form optimization, or optimum regulate thought and its functions to scientific and rehabilitation expertise, will locate this e-book valuable.

The first bankruptcy by way of Martin Burger presents an summary of contemporary advancements relating to Bregman distances, that's a huge instrument in inverse difficulties and photograph processing. The bankruptcy by way of Piotr Kalita reports the operator model of a primary order in time partial differential inclusion and its time discretization. within the bankruptcy by way of Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth form optimization difficulties for variational inequalities are thought of. the subsequent bankruptcy, via Katja Mombaur is dedicated to functions of optimum regulate and inverse optimum regulate within the box of scientific and rehabilitation expertise, specifically in human move research, remedy and development via scientific units. the ultimate bankruptcy, through Nikolai Osmolovskii and Helmut Maurer offers a survey on no-gap moment order optimality stipulations within the calculus of diversifications and optimum keep watch over, and a dialogue in their extra development.

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**Sample text**

Gradient Flows in Metric Spaces and in the Space of Probability Measures. Birkhaeuser, Basel/Boston/Berlin (2005) 2. : Entropy decay of discretized Fokker-Planck equations I: temporal semidiscretization. Comput. Math. Appl. 46, 1683–1690 (2003) Bregman Distances in Inverse Problems and Partial Differential Equations 31 3. : On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Commun. Partial Differ. Equ. 26, 43–100 (2001) 4. : Entropies and equilibria of many-particle systems: an essay on recent research.

N→∞ k→∞ Theorem 2. Let I be an open and finite time interval and let X be a reflexive Banach space. Let f ∈ L1 (I; X) and let {fn }∞ n=1 be a sequence of functions from Attractors for Parabolic Inclusions 39 L1 (I; X) such that fn → f weakly in L1 (I; X). e. t ∈ I we have fn (t) X ≤ Rt , where Rt is a positive constant independent of n, but possibly dependent on t ∈ I. e. n→∞ t ∈ I. If (X, · X ) is a Banach space, then we define the distance from the point x ∈ X to the set A ⊂ X as distX (x, A) = infy∈A x − y X .

Nonsmooth analysis of doubly nonlinear evolution equations. Calc. Var. Partial Differ. Equ. 46, 253–310 (2013) 47. : Multiscale methods for polyhedral regularizations and applications in high dimensional imaging. D. thesis, University of Muenster (2012) 48. : Multiscale methods for polyhedral regularizations. SIAM J. Optim. 23, 1424–1456 (2013) 49. : Reconstruction of short time PET scans using Bregman iterations. In: Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), pp. 2383–2385.

### Advances in Mathematical Modeling, Optimization and Optimal Control by Jean-Baptiste Hiriart-Urruty, Adam Korytowski, Helmut Maurer, Maciej Szymkat

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