Gaussian mixture model (GMM) – Optimization Online

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Published: 2026/07/18

Shibshankar Dey

Nonlinear Optimization, Robust Optimization, Stochastic Programming chance constraint, Gaussian mixture model (GMM), optimal transport, out-of-sample performance, wasserstein distance

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

On Solving Chance-Constrained Models with Gaussian Mixture Distribution

Published: 2025/11/22, Updated: 2026/07/18

Nonlinear Optimization, Stochastic Programming, Yield Management approximation accuracy, continuity, differentiability, finite breakpoints, Gaussian mixture model (GMM), piecewise linear (PWL), standard normal distribution

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise linear approximations of the standard normal cumulative density function. We show that $O\left(\sqrt{\ln(1/\tau)/\tau} \right)$ pieces are sufficient to attain $\tau$-accuracy in the chance constraint. … Read more