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Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel’s doctoral descendant tree 1983–2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren, and 2 great-great-grandchildren, a total of 139 doctoral descendants.  This book starts with a personal tribute to Martin Grötschel by the editors (Part I), a contribution by his very special “predecessor” Manfred Padberg on “Facets and Rank of Integer Polyhedra” (Part II), and the doctoral descendant tree 1983–2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant.  The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, superclasses of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs, and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering.  Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions, and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization, and gas network optimization.  Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes.  The two closing articles are devoted to computational advances in general mixed-integer linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the “scientific facets” of Martin Grötschel who has set standards in theory, computation, and applications.

Combinatorial optimization. --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Mathematical optimization. --- Mathematics. --- Algorithms. --- Computational complexity. --- Optimization. --- Applications of Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Discrete Mathematics in Computer Science. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Foundations --- Applied mathematics. --- Engineering mathematics. --- Mathematical models. --- Computer science—Mathematics. --- Models, Mathematical --- Engineering --- Engineering analysis --- Mathematics --- Grötschel, Martin. --- Grötschel, M. --- Groetschel, Martin

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Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like - How can mathematics improve to the improvement of technological processes and products - What is happening already? - Where are the deficits? - What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.

Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Mathématiques --- Factors of production. --- Production functions (Economic theory) --- Production functions (Economic theory). --- Factors of production --- Business & Economics --- Engineering & Applied Sciences --- Economic Theory --- Applied Mathematics --- Engineering mathematics. --- Production (Economic theory) --- Engineering --- Engineering analysis --- Mathematics --- Mathematical models. --- Microeconomics --- Supply and demand --- Demand (Economic theory) --- Supply-side economics --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Math --- Science