Interior point methods for nonlinear programs (NLPs) are adapted for solution of mathematical programs with complementarity constraints (MPCCs). The constraints of the MPCC are suitably relaxed so as to guarantee a strictly feasible interior for the inequality constraints. The standard primal-dual algorithm has been adapted with a modified step calculation. The algorithm is shown to … Read more
We explicitly calculate universal barrier functions for cones generated by (weakly) Chebyshev systems over finite sets. We show that universal barrier functions corresponding to Chebyshev systems on intervals are obtained as limits of universal barrier functions of their discretizations. The results are heavily rely upon classical work of M. Krein, A. Nudelman and I.J. Schoenberg … Read more
In this paper we consider a particular class of nonlinear optimization problems involving both continuous and discrete variables. The distinguishing feature of this class of nonlinear mixed optimization problems is that the structure and the number of variables of the problem depend on the values of some discrete variables. In particular we define a general … Read more
We propose an algorithm based on Barvinok’s counting algorithm for P -> max {c’x | Ax