Restarting after branching in the SDP approach to MAX-CUT and similar combinatorial optimization problems

Journal of Combinatorial Optimization, 5(2), 2001, pages 151-166.

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Author:

John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
mitchj@rpi.edu

June 25, 1999.

Abstract:

Many combinatorial optimization problems have relaxations that are semidefinite programming problems. In principle, the combinatorial optimization problem can then be solved by using a branch-and-cut procedure, where the problems to be solved at the nodes of the tree are semidefinite programs. When branching, it is desirable to use the solution to the parent relaxation as a warm start for the child relaxation. We show that a new dual strictly feasible solution can be found in a straightforward manner. The branch-and-cut approach to mixed integer linear programming problems can be restarted at each node of the tree using the dual simplex method; our method for SDP branch-and-cut algorithms gives an analogous method for efficiently solving the child problems.

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