U. Aldasoro Marcellan, M. Merino Maestre
Stochastic Dominance is a prominent form of stochastic ordering in decision analysis. In the context of multistage optimization, it acts as a risk averse measure over the undesired tails. Most of the existing applications of Stochastic Dominance consider a single component linear function models. However, many real world applications, such as production planning, include quadratic costs or quadratic penalty terms. To tackle this situation, we present two novel approaches for the treatment of the quadratic terms: a combined mixed linear-quadratic dominance (labelled Coupled Stochastic Dominance) and a component-wise separated dominance (Decoupled Stochastic Dominance). Both are time consistent risk averse measures based on Expected Conditional Stochastic Dominance measures. The resulting quadratically constrained problems are computationally challenging for state-of-the-art solvers. Thus, a primal decomposition based matheuristic algorithm is proposed to solve such problems.
Keywords: Stochastic optimization, multistage, risk averse measures, decomposition algorithms
Scheduled
Continuous Optimization
June 10, 2022 4:00 PM
A12
