An application of an interior point method for problems with uncertainty

Interior point methods (IPM) were first proposed for linear programming (LP) problems. Since 1984, when Karmarkar published his famous paper (Karmarkar (1984)), IPM were rapidly developed and improved. It is now widely accepted that the primal-dual logarithmic barrier method is the most efficient IPM. The idea of IPM was not restricted to linear programming alone. These methods quickly spread to quadratic, nonlinear and integer programming. The developments in quadratic programming (QP) are closely parallel to those in LP. While theoretical worst-case behaviour for LP and QP are the same, QP problems are harder to solve in practice. The derivation of the higher order primal-dual method for QP is analogous to the derivation for the linear case presented in Mehrotra (1991) and implemented by Altman and Gondzio (1992)