Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.33946

An Intersection Cutting Plane Algorithm for Chance-Constrained Programs with Finite Support

Soumya Ranjan Pathy·Hamed Rahimian
View original source ↗Read source document ↗Export metadata ↓

Abstract

Standard Big-M mixed-integer programming reformulations of chance-constrained programs (CCPs) with finite support often yield weak linear relaxations and scale poorly as the number of scenarios increases. To address this limitation, we derive two families of intersection cuts from problem-specific S-free sets and develop decomposition-based branch-and-cut frameworks. The first one exploits the submodular structure of the scenario requirement function, while the second one uses probability covers. We propose hybrid separation strategies that combine classical mixing inequalities and quantile cuts with the proposed intersection cuts. Computational experiments on integrated production-distribution planning instances show that the proposed hybrid methods reduce computational time compared to pure methods.

Explore related subjects

math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Soumya Ranjan Pathy, Hamed Rahimian. 2026-09-27. An Intersection Cutting Plane Algorithm for Chance-Constrained Programs with Finite Support. https://arxiv.org/abs/2609.33946

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Verifiable constraint qualifications for infinite-dimensional optimization problems and their applications to optimal control problems

This paper employs a finite codimensionality condition to establish an enhanced Fritz John condition for general constrained nonlinear infinite-dimensional optimization problems. In applications, this approach provides a new, unified framework for deriving first-order necessary conditions across a broad class of optimal control problems involving both deterministic and stochastic systems. Compared to existing constraint qualifications, our finite codimensionality condition, which is equivalent to the validity of certain \textit{a priori} estimates, yields a direct and analytically tractable verification method for each application. Furthermore, the core ideas of this method can be further extended to investigate the KKT conditions for infinite-dimensional optimization problems.

math.OC↗
arXiv2026

Arrival-Intensity Control for A Single-Server Queue in Heavy Traffic

We study a single-server queue control problem (QCP) in a heavy-traffic regime, extending the framework from Lee and Weerasinghe (2011). The state process represents the offered waiting time. Service times and patience times form independent i.i.d. sequences with general distributions. We formulate an infinite-horizon discounted QCP that balances the cost of controlling the arrival intensity against a penalty for server idleness. A distinctive feature of the formulation is the nonstandard decreasing operational running cost arising from the arrival-intensity control mechanism. Under suitable heavy-traffic assumptions, the diffusion-scaled offered waiting-time process converges to a regulated diffusion, leading to an associated diffusion control problem (DCP). We find the optimal control of the associated DCP by incorporating the Legendre-Fenchel transform and a formal Hamilton-Jacobi-Bellman (HJB) equation. We then construct a sequence of intensity controls for the prelimit queueing systems from the DCP-optimal feedback and establish its asymptotic optimality within the specified heavy-traffic admissible control class. Beyond theoretical analysis, numerical experiments further examine whether reinforcement learning can approximate the optimal policy with discounted costs close to the HJB reference. Policies are trained from simulated state transitions and realized costs, and are evaluated against the independently computed HJB feedback.

math.OC↗
arXiv2026

Information-Theoretic Upper Bounds for Deterministic Noise in Zeroth-Order Convex Optimization

We study zeroth-order convex optimization on Euclidean balls with function values corrupted by a fixed, uniformly bounded deterministic perturbation. For a query budget $T$, the maximum admissible level of noise (MALN) is the supremum of noise levels for which an $\eps$-accurate solution can be found with probability $1-β$. We construct an explicit hard family: the support function of a spherical belt combined with an affine branch along a hidden random direction. It yields finite-budget upper bounds on the MALN for Lipschitz, strongly convex, uniformly convex, smooth, Hölder, and smooth strongly convex classes. For Lipschitz objectives the bound has order $\eps^2\sqrt\ell/(\sqrt nMR)+\eps\ell/n$, where $\ell=\log(2(T+1)/(1-β))$ and $n-1\ge32\ell$; this is the scale of Li and Risteski with explicit logarithmic factors. A tangential-gradient estimate for the Moreau envelope yields the smooth scale $\eps^{3/2}/(\sqrt n\sqrt L\,R)$ and, for $L-μ\ge5μ$, the smooth strongly convex scale $\eps\sqrt{μ/((L-μ)n)}$. These bounds are tight: on explicit parameter ranges and subclasses, polynomial-query two-point methods tolerate noise of the order of the terms of order $n^{-1/2}$, so that the MALN is determined up to $O(\sqrt\ell)$ and absolute constants whenever these terms dominate. At $L=μ$, simplex interpolation with $n+1$ queries tolerates noise $R\sqrt{2μ\eps/n}$, which is optimal up to $O(\sqrt\ell)$ for $\eps\leμR^2/3$, while with at most $n$ exact queries no randomized algorithm guarantees success probability greater than $1/2$ uniformly over the class. We also quantify noise tolerance near this endpoint and illustrate the hiding mechanism and the breakdown of a two-point method numerically.

math.OC↗