26-02-2026 / 15:00 / CORE C.035

Marius Roland

(INRIA Lille)

will give a presentation on 

On Multidimensional Disjunctive Inequalities for Chance-Constrained Stochastic Problems with Finite Support

Abstract:

"This presentation addresses linear Chance-Constrained Stochastic Problems (CCSPs) with finite support. We begin by motivating the study of CCSPs through illustrative examples and providing intuition regarding the concept of feasibility in this context. Subsequently, we discuss the computational challenges inherent to these problems, specifically the nonconvex structure of the feasible region and the limitations of the standard big-M reformulation. These challenges necessitate the use of branch-and-cut approaches.
To this end, we review existing families of valid inequalities, such as quantile inequalities [1] and mixing inequalities [2]. This background sets the stage for the primary contribution of this work: a new class of valid inequalities termed multi-disjunctive inequalities. We construct these inequalities by exploiting a disjunctive property inherent to the mathematical formulation of CCSPs. Theoretical analysis reveals that the closure of these multi-disjunctive inequalities constitutes a proper subset of the closure generated by previously proposed families.
We perform numerical experiments within a pure cutting-plane framework to compare the closures obtained by enumerating all violated valid inequalities. The results demonstrate that multi-disjunctive inequalities significantly strengthen the continuous relaxation of the considered CCSPs compared to existing quantile and mixing-set inequalities. Furthermore, we evaluate the performance of these inequalities embedded within a branch-and-cut framework. Our results indicate that the proposed approach significantly outperforms existing methods on both standard
literature instances and newly generated instances designed to be computationally challenging. 
[1] W. Xie and S. Ahmed, On quantile cuts and their closure for chance constrained optimization problems, Mathematical Programming, 172 (2018), pp. 621-64
[2]  J. Luedtke, S. Ahmed, and G. L. Nemhauser, An integer programming approach for linear programs with probabilistic constraints, Mathematical Programming 122 (2010), pp. 247- 272"

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