A Coordinate Ascent Method for Solving Semidefinite Relaxations of Non-convex Quadratic Integer Programs

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• 关键词：Semidefinite programming ; Non ; convex quadratic integer optimization ; Coordinate descent method
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9849
• 期：1
• 页码：110-122
• 全文大小：321 KB
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• 作者单位：Christoph Buchheim (16)
  Maribel Montenegro (16)
  Angelika Wiegele (17)
  
  16. Fakultät für Mathematik, Technische Universität Dortmund, Dortmund, Germany
  17. Department of Mathematics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria
  
• 丛书名：Combinatorial Optimization
• ISBN：978-3-319-45587-7
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9849

文摘

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and by low-rank constraint matrices. We exploit this special structure by solving the dual problem, using a barrier method in combination with a coordinate-wise exact line search. The main ingredient of our algorithm is the computationally cheap update at each iteration and an easy computation of the exact step size. Compared to interior point methods, our approach is much faster in obtaining strong dual bounds. Moreover, no explicit separation and reoptimization is necessary even if the set of primal constraints is large, since in our dual approach this is covered by implicitly considering all primal constraints when selecting the next coordinate.