A second-order cone programming approach for linear programs with joint probabilistic constraints

This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.