Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings

• Published in: Mathematical programming Vol. 198; no. 1; pp. 997 - 1058
• Main Authors: Cartis, Coralia, Massart, Estelle, Otemissov, Adilet
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2023; Springer; Springer Nature B.V
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Constraints; Feasibility; Full Length Paper; Global optimization; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Polynomials; Subspaces; Theoretical; 49K45; 15A52; Global optimization; Dimensionality reduction techniques; 65K05; 90C30; Random embeddings; 90C26; Constrained optimization; Functions with low effective dimensionality

We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore the intrinsic low dimensionality of the constrained landscap...