CPLEX

CPLEX is a solver for linear, mixed-integer and quadratic programming problems developed by ILOG (http://www.ilog.com/products/cplex/).  CPLEX contains a primal simplex algorithm, a dual simplex algorithm, a network optimizer, an interior point barrier algorithm, a mixed integer algorithm and a quadratic capability.  CPLEX also contains an infeasibility finder.  For problems with integer variables, CPLEX uses a branch and bound algorithm (with cuts) and supports specially ordered set variables SOS1, SOS2 as well as semi-continuous and semi-integer variables.  Base CPLEX solves LP and RMIP model types.  Additional capabilities of CPLEX can be licensed involving Barrier, MIP and QCP capability.  The write-up for CPLEX is on CPLEX.pdf.

A bare bones free version is available as OSICPLEX.