Nonlinear stochastic programming - with a case study in continuous switching

The optimal solution, as well as the objective of stochastic programming problems vary with the underlying probability measure. This paper addresses stability with respect to the underlying probability measure and stability of the objective. The techniques presented are employed to make problems numerically tractable, which are formulated by involving numerous scenarios, or even by involving a continuous probability measure. The results justify clustering techniques, which significantly reduce computation times while guaranteeing a desired approximation quality. The second part of the paper highlights Newton’s method to solve the reduced stochastic recourse problems. The techniques presented exploit the particular structure of the recourse function of the stochastic optimization problem. The tools are finally demonstrated on a benchmark problem, which is taken from electrical power flows