A bound for the Symmetric Travelling Salesman problem through matroid formulation

Article Abstract:

A bound for the Symmetric Traveling Salesman Problem (TSP) is developed. The Symmetric TSP is modeled as a matroid intersection problem with parity conditions. The new model also provides a relaxation of the problem and establishes a link between the well-studied 1-tree and 2-matching bounds. An algorithm to determine the lower bound provided by the relaxation is also discussed.

Models, Combinatorial optimization, Traveling-salesman problem

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Semidefinite descriptions of cones defining spectral mask constraints

Article Abstract:

The structural details of trigonometric polynomial cones are described in terms of semidefinite constraints.

United States, Trigonometrical functions, Trigonometric functions

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On the optimal parameter of a self-concordant barrier over a symmetric cone

Article Abstract:

The properties of self-concordant barriers are presented with reference to symmetric cones.

Portugal, Methods, Structural optimization

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