TA10 - Stochastic and Robust Optimization 2

In this talk, we investigate stochastic optimal control problems for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the existence and uniqueness of the solutions of a new type of McKean-Vlasov equations driven by both jump and switching processes and derive a relevant version of Ito’s formula. We provide the dynamic programming principle and prove a verification theorem for the associated control problem. In addition, a stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle.

This study formulates a two-stage mixed-integer stochastic program to improve the integrated protection and restoration of interdependent infrastructure networks. The first stage concerns binary decisions on which components to fortify, while the second stage addresses mixed-integer decisions on the repair-crew schedule, network flow, etc. We propose using enhanced Lagrangian cuts and strengthened Benders cuts to solve the two-stage stochastic mixed-integer program. To address the cut-generation efficiency issue when the subproblem is large-scale, we propose a multi-stage reformulation and compare the stochastic dual dynamic programming algorithm with its two-stage counterpart. Synthetic interdependent networks are employed to illustrate the proposed stochastic program and the solution method. The computational results also reveal the topological structure of cutting planes required for fast convergence.

End-of-first-life LIBs retain capacity yet are routinely discarded. This study develops a two-stage stochastic MILP embedding IoT diagnostics into a circular reverse logistics network. Strategic facility decisions use aggregated SoH distributions; weekly operational triage responds to observed battery condition at arrival. Three objectives are balanced: cost, gate-to-gate GHG, and avoided DALYs from reduced virgin-material extraction.

Scenario-based stochastic programming often becomes intractable when second-stage problems are combinatorial and NP-hard. We develop a GPU-based, scenario-batched dynamic programming framework that enables large-scale evaluation of full-fidelity integer recourse models. The approach achieves orders-of-magnitude speedups, allowing far larger scenario sets and significantly improving first-stage decision quality.

**Keywords:** Stochastic programming; GPU acceleration; Dynamic programming