Is there any linear programing solver, written for MATLAB, that (a) solves with the primal-dual interior point method, (b) the user has the options to set the target barrier parameter (he lowest value of barrier parameter for which the KKT system is solved)?
I currently use IPOPT, which has the target barrier parameter options. However, at convergence, the product of dual*slack seems to only be approximately satisfied (with an error of say (+-)1e-7 for a target parameter of 1e-5). I have tried to play around with the tolerances, but to no avail.
For MATLAB use, I recommend using CVX, which includes Gurobi, MOSEK, GLPK, and SDPT3. All of those can solve the linear program very efficiently.
CVX is very easy to use in MATLAB.