Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

Statistical-mechanical Analysis of Linear Programming Relaxation for Combinatorial Optimization Problems

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechan...

Typical behavior of the linear programming method for combinatorial optimization problems: From a statistical-mechanical perspective

Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a lattice-gas model on the Erdös-Rényi random graphs is analyzed by a replica method. It is found that the LP optimal solution is typically equal to that of the IP bel...

Linear, Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems

SENSITIVITY ANALYSIS IN LINEAR-PLUS-LINEAR FRACTIONAL PROGRAMMING PROBLEMS

In this paper, we study the classical sensitivity analysis when the right - hand – side vector, and the coefficients of the objective function are allowed to vary. 

Combinatorial Optimization and Integer Linear Programming Combinatorial Optimization

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