dimensionality reduction – Optimization Online

Optimized Dimensionality Reduction for Moment-based Distributionally Robust Optimization

Published: 2023/05/06

Optimization in Data Science, Robust Optimization, Semi-definite Programming data-driven optimization, dimensionality reduction, distributionally robust optimization, principal component analysis, semidefinite programming

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint distribution of random parameters runs in a distributional ambiguity set constructed by moment information and makes decisions against the worst-case distribution within the set. Although most moment-based DRO problems … Read more

Global optimization using random embeddings

Published: 2021/07/24

Coralia Cartis

Estelle Massart

Adilet Otemissov

Global Optimization, Nonlinear Optimization conic integral geometry, dimensionality reduction, functions with low effective dimension, global optimization, random subspaces

We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geometry. X-REGO randomly projects, in a sequential or simultaneous manner, the high- dimensional original problem into low-dimensional subproblems that can then be solved with any global, or even local, optimization solver. We estimate … Read more