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Program."],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 landscape using feasible random embeddings, in order to understand and improve the scalability of algorithms for the global optimization of these special-structure problems. A reduced subproblem formulation is investigated that solves the original problem over a random low-dimensional subspace subject to affine constraints, so as to preserve feasibility with respect to the given domain. Under reasonable assumptions, we show that the probability that the reduced problem is successful in solving the original, full-dimensional problem is positive. Furthermore, in the case when the objective\u2019s effective subspace is aligned with the coordinate axes, we provide an asymptotic bound on this success probability that captures its polynomial dependence on the effective and, surprisingly, ambient dimensions. We then propose X-REGO, a generic algorithmic framework that uses multiple random embeddings, solving the above reduced problem repeatedly, approximately and possibly, adaptively. Using the success probability of the reduced subproblems, we prove that X-REGO converges globally, with probability one, and linearly in the number of embeddings, to an <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03f5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighbourhood of a constrained global minimizer. Our numerical experiments on special structure functions illustrate our theoretical findings and the improved scalability of X-REGO variants when coupled with state-of-the-art global\u2014and even local\u2014optimization solvers for the subproblems.\n<\/jats:p>","DOI":"10.1007\/s10107-022-01812-9","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T02:03:29Z","timestamp":1652493809000},"page":"997-1058","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings"],"prefix":"10.1007","volume":"198","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0963-5550","authenticated-orcid":false,"given":"Coralia","family":"Cartis","sequence":"first","affiliation":[]},{"given":"Estelle","family":"Massart","sequence":"additional","affiliation":[]},{"given":"Adilet","family":"Otemissov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"1812_CR1","volume-title":"Tapas in Experimental Mathematics, Contemporary Mathematics","year":"2008","unstructured":"Amdeberhan, T., Moll, V.H. 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