Facets of Combinatorial Optimization, 1st Edition

  • Published By:
  • ISBN-10: 3642381898
  • ISBN-13: 9783642381898
  • DDC: 519.6
  • Grade Level Range: College Freshman - College Senior
  • 506 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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, super classes 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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Martin Grötschel—Activist in Optimization.
2: Martin Grötschel—The Early Years in Bonn and Augsburg.
3: Contribution by a Very Special Predecessor of Martin Grötschel.
4: Facets and Rank of Integer Polyhedra.
5: Martin Grötschel's Doctoral Descendants.
6: Martin Grötschel's Descendants and Their Doctoral Theses 1983–2012.
7: Contributions by Martin Grötschel's Doctoral Descendants.
8: Constructing Extended Formulations from Reflection Relations.
9: Mirror-Descent Methods in Mixed-Integer Convex Optimization.
10: Beyond Perfection: Computational Results for Superclasses.
11: From Vertex-Telecenters to Subtree-Telecenters.
12: Algorithms for Junctions in Acyclic Digraphs.
13: Algorithms for Scheduling Sensors to Maximize Coverage Time.
14: How Many Steiner Terminals Can You Connect in 20 Years?.
15: The Maximum Weight Connected Subgraph Problem.
16: Exact Algorithms for Combinatorial Optimization Problems with Submodular Objective Functions.
17: A Primal Heuristic for Nonsmooth Mixed Integer Nonlinear Optimization.
18: A New Algorithm for MINLP Applied to Gas Transport Energy Cost Minimization.
19: Solving k-Way Graph Partitioning Problems to Optimality: The Impact of Semidefinite Relaxations and the Bundle Method.
20: On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control.
21: Scheduling and Routing of Fly-in Safari Planes Using a Flow-over-Flow Model.
22: Mixed Integer Programming: Analyzing 12 Years of Progress.
23: Progress in Academic Computational Integer Programming.