Výsledky vyhledávání

Autor: Ky Khac Vu, Pierre-Louis Poirion, Leo Liberti

Publikováno v: Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2021, 626, pp.204-220. ⟨10.1016/j.laa.2021.06.010⟩

International audience; We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formall

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd94f715f38fcca55d046c9acfe305e8
http://arxiv.org/abs/2101.04182

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Random projections for quadratic programs

Autor: Ky Khac Vu, Claudia D’Ambrosio, Leo Liberti, Pierre-Louis Poirion

Publikováno v: Mathematical Programming
Mathematical Programming, Springer Verlag, In press, 183, pp.619-647. ⟨10.1007/s10107-020-01517-x⟩

International audience; Random projections map a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Although random projections are usually applied to numerical data,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d688228debad9bed78d861f20c88c012
https://hal.archives-ouvertes.fr/hal-02869240

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Barvinok’s naive algorithm in Distance Geometry

Autor: Leo Liberti, Ky Khac Vu

Publikováno v: Operations Research Letters
Operations Research Letters, Elsevier, 2018, 46 (5), pp.476-481. ⟨10.1016/j.orl.2018.06.006⟩

International audience; In 1997, A. Barvinok gave a probabilistic algorithm to derive a near-feasible solution of a quadratically (equation) constrained problem from its semidefinite relaxation. We generalize this algorithm to handle matrix variables

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bca5dbc9947af90df5c05a35e07bbd60
https://doi.org/10.1016/j.orl.2018.06.006

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A FORMAL PROOF OF THE KEPLER CONJECTURE

Publikováno v: Forum of Mathematics. Pi, 5, 1-29
Forum of Mathematics. Pi, 5, pp. 1-29
Forum of Mathematics, Pi

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a280db53ee95a279e1aa5fc6830335ea
https://hdl.handle.net/2066/176365

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Gaussian random projections for Euclidean membership problems

Autor: Pierre-Louis Poirion, Leo Liberti, Ky Khac Vu

Publikováno v: Discrete Applied Mathematics
Discrete Applied Mathematics, Elsevier, 2019, 253, pp.93-102. ⟨10.1016/j.dam.2018.08.025⟩

International audience; We discuss the application of Gaussian random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. In particular, we consider the two cases, when the target set

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::850fe4a6f1fe144821b5ea4223bef4e3
https://hal.archives-ouvertes.fr/hal-02105075

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Random Projections for Quadratic Programs over a Euclidean Ball

Autor: Ky Khac Vu, Leo Liberti, Pierre-Louis Poirion, Claudia D’Ambrosio

Publikováno v: Integer Programming and Combinatorial Optimization (IPCO)
Integer Programming and Combinatorial Optimization (IPCO), 2019, Ann Arbor, United States. pp.442-452, ⟨10.1007/978-3-030-17953-3_33⟩
Integer Programming and Combinatorial Optimization ISBN: 9783030179526
IPCO

International audience; Random projections are used as dimensional reduction techniques in many situations. They project a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean dist

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f07c33733cc51ee1577a7a810a029241
https://hal.archives-ouvertes.fr/hal-02869206/document

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Surrogate-based methods for black-box optimization

Autor: Claudia D’Ambrosio, Ky Khac Vu, Leo Liberti, Youssef Hamadi

Publikováno v: International Transactions in Operational Research. 24:393-424

In this paper, we survey methods that are currently used in black-box optimization, i.e. the kind of problems whose objective functions are very expensive to evaluate and no analytical or derivative information are available. We concentrate on a part

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b838435254760349199789c1d9b0414e
https://doi.org/10.1111/itor.12292

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Random Projections for Linear Programming

Autor: Ky Khac Vu, Pierre-Louis Poirion, Leo Liberti

Publikováno v: Mathematics of Operations Research
Mathematics of Operations Research, INFORMS, 2018, 43 (4), pp.1051-1071. ⟨10.1287/moor.2017.0894⟩

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known Johnson-Lindenstrau

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a397d767bee2029cd2fa1970eb04b29c
https://hal.archives-ouvertes.fr/hal-02105076/document

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New Error Measures and Methods for Realizing Protein Graphs from Distance Data

Autor: Leo Liberti, Carlile Lavor, Nelson Maculan, Ky Khac Vu, Claudia D’Ambrosio

Publikováno v: Discrete and Computational Geometry
Discrete and Computational Geometry, Springer Verlag, 2017, 57 (2), pp.371-418. ⟨10.1007/s00454-016-9846-7⟩

International audience; The interval Distance Geometry Problem (i DGP) consists in finding a realization in R K of a simple undirected graph G = (V, E) with nonnegative intervals assigned to the edges in such a way that, for each edge, the Euclidean

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c85ec1a8098703014d4c63a63805ac94
https://hal.archives-ouvertes.fr/hal-02105303/document

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