An Adjustable Robust Two-stage Stochastic Quadric Programming and its Solution with Subgradient Algorithms

Robust stochastic optimization provides a worst-case decision-making scheme under uncertain probability distributions, but the results could be too conservative and pessimistic. This paper establishes a class of adjustable robust two-stage stochastic quadratic programming based on a parameter-related affine uncertain set. The convexity of the problem is verified, and the subdifferential is obtained. An improved subgradient algorithm is proposed for solving the problem based on a deflected subgradient direction and a step-size strategy with exponential decay. The convergence of the algorithm is proved, and the numerical examples demonstrate the effectiveness. The calculation results show that the adjustable robust stochastic programming is related to the parameter-related, and the optima value decreases as the parameter increases. The approach can provide decision-makers with more optimistic solutions besides the worst-case ones.