a homogeneous predictor-corrector algorithm for stochastic nonsymmetric convex conic optimization with discrete support

We consider a stochastic convex optimization problem over nonsymmetric cones with discrete support. this class of optimization problems has not been studied yet. by using a logarithmically homogeneous self-concordant barrier function, we present a homogeneous predictor-corrector interior-point algorithm for solving stochastic nonsymmetric conic optimization problems. we also derive an iteration bound for the proposed algorithm. our main result is that we uniquely combine a nonsymmetric algorithm with efficient methods for computing the predictor and corrector directions. finally, we describe a realistic application and present computational results for instances of the stochastic facility location problem formulated as a stochastic nonsymmetric convex conic optimization problem.