A second-order sufficient optimality condition for risk-neutral bi-level stochastic linear programs (Q2026728)

In this paper the author derives sufficient optimality conditions for Lipschitz continuity of the gradient of the expectation functional arising from a bi-level stochastic linear program with random right-hand side in the lower-level constraint system. His main result is used to formulate a second-order sufficient optimality condition for risk-neutral bi-level stochastic linear programs in terms of the generalized Hessians. The author also studies geometric properties of regions of strong stability and derives representation results, which may facilitate the computation or sample-based estimation of gradients of the expectation functional, which enhances gradient descent-based methods.