3 Search Results for "Roche-Newton, Oliver"

Document

DOI: 10.4230/LIPIcs.SEA.2024.16

Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods

Authors: Deborah Hendrych, Mathieu Besançon, and Sebastian Pokutta

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract

We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances.

Cite as

Deborah Hendrych, Mathieu Besançon, and Sebastian Pokutta. Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hendrych_et_al:LIPIcs.SEA.2024.16,
  author =	{Hendrych, Deborah and Besan\c{c}on, Mathieu and Pokutta, Sebastian},
  title =	{{Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.16},
  URN =		{urn:nbn:de:0030-drops-203810},
  doi =		{10.4230/LIPIcs.SEA.2024.16},
  annote =	{Keywords: Mixed-Integer Non-Linear Optimization, Optimal Experiment Design, Frank-Wolfe, Boscia}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2018.69

An Improved Bound for the Size of the Set A/A+A

Authors: Oliver Roche-Newton

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract

It is established that for any finite set of positive real numbers A, we have |A/A+A| >> |A|^{3/2+1/26} / log^{5/6}|A|.

Cite as

Oliver Roche-Newton. An Improved Bound for the Size of the Set A/A+A. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 69:1-69:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{rochenewton:LIPIcs.SoCG.2018.69,
  author =	{Roche-Newton, Oliver},
  title =	{{An Improved Bound for the Size of the Set A/A+A}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{69:1--69:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.69},
  URN =		{urn:nbn:de:0030-drops-87820},
  doi =		{10.4230/LIPIcs.SoCG.2018.69},
  annote =	{Keywords: sum-product estimates, expanders, incidence theorems, discrete geometry}
}

Document

DOI: 10.4230/LIPIcs.SOCG.2015.74

A Short Proof of a Near-Optimal Cardinality Estimate for the Product of a Sum Set

Authors: Oliver Roche-Newton

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract

In this note it is established that, for any finite set A of real numbers, there exist two elements a, b from A such that |(a + A)(b + A)| > c|A|^2 / log |A|, where c is some positive constant. In particular, it follows that |(A + A)(A + A)| > c|A|^2 / log |A|. The latter inequality had in fact already been established in an earlier work of the author and Rudnev, which built upon the recent developments of Guth and Katz in their work on the Erdös distinct distance problem. Here, we do not use those relatively deep methods, and instead we need just a single application of the Szemerédi-Trotter Theorem. The result is also qualitatively stronger than the corresponding sum-product estimate from the paper of the author and Rudnev, since the set (a + A)(b + A) is defined by only two variables, rather than four. One can view this as a solution for the pinned distance problem, under an alternative notion of distance, in the special case when the point set is a direct product A x A. Another advantage of this more elementary approach is that these results can now be extended for the first time to the case when A is a set of complex numbers.

Cite as

Oliver Roche-Newton. A Short Proof of a Near-Optimal Cardinality Estimate for the Product of a Sum Set. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 74-80, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{rochenewton:LIPIcs.SOCG.2015.74,
  author =	{Roche-Newton, Oliver},
  title =	{{A Short Proof of a Near-Optimal Cardinality Estimate for the Product of a Sum Set}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{74--80},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.74},
  URN =		{urn:nbn:de:0030-drops-51200},
  doi =		{10.4230/LIPIcs.SOCG.2015.74},
  annote =	{Keywords: Szemer\'{e}di-Trotter Theorem, pinned distances, sum-product estimates}
}

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