EUROPT 2025
Abstract Submission

504. Presolve techniques for quasi-convex chance constraints with finite-support low-dimensional uncertainty

Invited abstract in session TC-6: Structured nonsmooth optimization -- Part I, stream Nonsmooth and nonconvex optimization.

Tuesday, 14:00-16:00
Room: B100/7013

Authors (first author is the speaker)

1. Guillaume Van Dessel
Mathematical Engineering, UCLouvain
2. François Glineur
ICTEAM/INMA & CORE, Université catholique de Louvain (UCLouvain)

Abstract

Chance-constrained programs (CCP) represent a trade-off
between conservatism and robustness in optimization. In many CCPs,
one optimizes an objective under a probabilistic constraint continuously
parameterized by a (random) vector. In this work, we study the case where
the constraint is a quasi-convex function of this vector. Moreover, vector's
support is a collection of N scenarios in dimension p = 2 or p = 3.
In general, even when both the constraint and the objective are convex
in the decision variable, the feasible region of a CCP is nonconvex, turn-
ing it into a difficult problem. However, under mild assumptions, many
CCPs can be recast as big-M mixed-integer convex programs (MICP).
Unfortunately, the difficulty of these MICPs explodes with the number
of scenarios, restricting the instances practically solvable in decent time.
To cut down the effective number of scenarios considered in MICP re-
formulations and accelerate their solving, we propose and test presolve
techniques based on computational geometry. Our techniques produce
certificates to discard or select a priori some scenarios before solving
a regular MICP. Moreover, the information aggregated during presolve
leverages the possibility to strengthen big-M constants. Our numerical
experiments suggest that spending some time in presolve is more effi-
cient than a direct solve for a class of probabilistic projection problems,
including an interesting type of facility location problem

Keywords

Status: accepted

Back to the list of papers