J. Castro Pérez, L. F. Escudero Bueno, J. F. Monge Ivars
In a previous paper, the authors presented a novel approach based on an interior-point method (IPM) for solving large-scale multistage stochastic optimization problems. This approach considered both strategic and operational uncertainties.This work extends the previous approach by adding risk-averse constraints: either expected conditional value-at-risk or expected conditional stochastic dominance. As in the earlier risk-neutral approach, the new model is reformulated using splitting variables. The reformulated model remains compatible with the specialized IPM, which computes the Newton direction by combining Cholesky factorizations with preconditioned conjugate gradients (PCG). The new risk-averse constraints simply extend the preconditioner of the PCG with an additional diagonal matrix, preserving the efficient solution of systems with the preconditioner. Preliminary results are reported for the solution of real-world problems of several million variables and constraints.
Keywords: Large-scale optimization, Interior-point methods, Multistage stochastic optimization, CVaR and Stochastic Dominance risk averse functional, strategic and operational uncertainties
Scheduled
Continuous Optimization II
June 10, 2025 3:30 PM
MR 3