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

ISBN-10: 3319307843

ISBN-13: 9783319307848

ISBN-10: 3319307851

ISBN-13: 9783319307855

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

The first bankruptcy by way of Martin Burger presents an outline of modern advancements on the topic of Bregman distances, that's a tremendous software in inverse difficulties and photo 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 via Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth form optimization difficulties for variational inequalities are thought of. the following bankruptcy, by way of Katja Mombaur is dedicated to functions of optimum regulate and inverse optimum keep watch over within the box of scientific and rehabilitation expertise, particularly in human stream research, remedy and development by way of scientific units. the ultimate bankruptcy, by way of Nikolai Osmolovskii and Helmut Maurer presents a survey on no-gap moment order optimality stipulations within the calculus of diversifications and optimum keep an eye on, and a dialogue in their additional development.

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Math. Comput. 84, 1217–1240 (2015) 7. , Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37, A1111–A1138 (2015) 8. : Error estimates for general fidelities. Electron. Trans. Numer. Anal. 38, 44–68 (2011) 9. : Ground states and singular vectors of convex variational regularization methods. Methods Appl. Anal. 20, 295–334 (2013) 10. : Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Nonlinearity 27, 2111 (2014) 11. : The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming.

Ii) F satisfies the growth condition ξ U ∗ ≤ c(1 + u p−1 U ) for all u ∈ U and ξ ∈ F(u) with the constant c > 0. (iii) Graph of F is a sequentially closed set in (strong − U) × (weak − U ∗ ) topology. (iv) F satisfies the dissipativity condition ξ , u U ∗ ×U ≥ c1 −c2 u pU for all u ∈ U and ξ ∈ F(u) with c1 ∈ R and 0 ≤ c2 < ια p . (H0 ) f ∈ V ∗ , u0 ∈ H. H(U) For all finite time intervals I the Nemytskii mapping for ι denoted as ι¯ : M p,q (I; V, V ∗ ) → U (I) is compact. Remark 1. Note that assumption H(U) is motivated by Proposition 2 in [15].

Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37, A1111–A1138 (2015) 8. : Error estimates for general fidelities. Electron. Trans. Numer. Anal. 38, 44–68 (2011) 9. : Ground states and singular vectors of convex variational regularization methods. Methods Appl. Anal. 20, 295–334 (2013) 10. : Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Nonlinearity 27, 2111 (2014) 11. : The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming.

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