Convex Combinatorial Optimization

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Reference Work Entry
Convex Discrete Optimization
Shmuel Onn
2009, Encyclopedia of Optimization, Part 3, Pages 513-550
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The use of edge-directions and linear programming to enumerate vertices
Shmuel Onn and Uriel G. Rothblum
Journal of Combinatorial Optimization, 2007, Volume 14, Numbers 2-3, Pages 153-164
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Journal Article
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Yu. A. Kochetov
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Number 5, Pages 747-763
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A class of polynomial primal-dual interior-point algorithms for semidefinite optimization
Guo-qiang Wang and Yan-qin Bai
Journal of Shanghai University (English Edition), 2006, Volume 10, Number 3, Pages 198-207
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Book Chapter
On the Relative Complexity of 15 Problems Related to 0/1-Integer Programming
Andreas S. Schulz
2009, Research Trends in Combinatorial Optimization, Pages 399-428
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Discrete optimization
V. K. Leont’ev
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Number 2, Pages 328-340
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Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization
E. A. Yildirim
Journal of Optimization Theory and Applications, 2004, Volume 122, Number 2, Pages 405-423
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A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization
Min Zhang, Yan-qin Bai and Guo-qiang Wang
Journal of Shanghai University (English Edition), 2008, Volume 12, Number 6, Pages 475-480
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Journal Article
Speeding up IP-based algorithms for constrained quadratic 0–1 optimization
Christoph Buchheim, Frauke Liers and Marcus Oswald
Mathematical Programming, 2010, Volume 124, Numbers 1-2, Pages 513-535
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Journal Article
Randomized methods based on new Monte Carlo schemes for control and optimization
Boris T. Polyak and Elena N. Gryazina
Annals of Operations Research, 2011, Volume 189, Number 1, Pages 343-356
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Abstract

We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

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Convex Combinatorial Optimization

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