Optimizing over Semimetric Polytopes

Let G=(V,E) be a complete graph. Then the semimetric polytope \({\cal M}(G)\) associated with G is defined by the following system of inequalities called the triangle inequalities.

[1]  Panos M. Pardalos,et al.  Computational aspects of a branch and bound algorithm for quadratic zero-one programming , 1990, Computing.

[2]  Ali Ridha Mahjoub,et al.  On the cut polytope , 1986, Math. Program..

[3]  Dorit S. Hochbaum,et al.  Monotonizing linear programs with up to two nonzeroes per column , 2004, Oper. Res. Lett..

[4]  Francisco Barahona,et al.  The volume algorithm: producing primal solutions with a subgradient method , 2000, Math. Program..

[5]  Mihalis Yannakakis,et al.  Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract) , 1992, ICALP.

[6]  D. R. Fulkerson,et al.  Some Properties of Graphs with Multiple Edges , 1965, Canadian Journal of Mathematics.

[7]  Antonio Frangioni,et al.  A Computational Study of Cost Reoptimization for Min-Cost Flow Problems , 2006, INFORMS J. Comput..

[8]  F. B A R A H O N A,et al.  EXPERIMENTS IN QUADRATIC 0-1 PROGRAMMING , 2005 .

[9]  Antonio Frangioni,et al.  Generalized Bundle Methods , 2002, SIAM J. Optim..

[10]  Francisco Barahona,et al.  Network Design Using Cut Inequalities , 1996, SIAM J. Optim..

[11]  Michel Deza,et al.  Geometry of cuts and metrics , 2009, Algorithms and combinatorics.

[12]  Oktay Günlük,et al.  Minimum cost capacity installation for multicommodity network flows , 1998, Math. Program..

[13]  A. K. Mittal,et al.  Unconstrained quadratic bivalent programming problem , 1984 .

[14]  Andrew V. Goldberg,et al.  An efficient implementation of a scaling minimum-cost flow algorithm , 1993, IPCO.

[15]  A. Löbel Solving Large-Scale Real-World Minimum-Cost Flow Problems by a Network Simplex Method , 1996 .

[16]  Nelson Maculan,et al.  The volume algorithm revisited: relation with bundle methods , 2002, Math. Program..