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Exploiting Constant Trace Property in Large-scale Polynomial Optimization

Autor: Ngoc Hoang Anh Mai, J. B. Lasserre, Victor Magron, Jie Wang

Publikováno v: ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software, 2022, 48 (4), pp.1-39. ⟨10.1145/3555309⟩

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such moment relaxati

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80b26dd1f03f112e54818c7b7f95d691
https://doi.org/10.1145/3555309

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Akademický článek

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Optimization of Polynomials with Sparsity Encoded in a Few Linear Forms

Autor: Jean B. Lasserre

Publikováno v: IFAC-PapersOnLine. 55:383-387

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::66579a64911f2c59a7a7038d0102662c
https://doi.org/10.1016/j.ifacol.2022.11.083

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Akademický článek

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Akademický článek

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Positivity certificates and polynomial optimization on non-compact semialgebraic sets

Autor: Victor Magron, Ngoc Hoang Anh Mai, Jean B. Lasserre

Publikováno v: Mathematical Programming, Series A
Mathematical Programming, Series A, 2021, ⟨10.1007/s10107-021-01634-1⟩
Mathematical Programming, Series A, Springer, 2021, ⟨10.1007/s10107-021-01634-1⟩

In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu [Comptes Rendus de l'Acad\'emie des Sciences-Series I-Mathematics, 328(6) (1999) pp. 495-499]. We use J

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::73b3202770b36fc24eca8e8af01c4f9a
https://doi.org/10.1007/s10107-021-01634-1

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Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension

Autor: Jie Wang, Victor Magron, Jean B. Lasserre

Publikováno v: SIAM Journal on Optimization
SIAM Journal on Optimization, 2021, ⟨10.1137/20M1323564⟩
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2021, ⟨10.1137/20M1323564⟩

This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sparse moment-SOS framework based on term-sparsity and chordal extension

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8fb6a9266c8e08e9ac7303bab91dc323
https://doi.org/10.1137/20m1323564

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A Sublevel Moment-SOS Hierarchy for Polynomial Optimization

Autor: Tong Chen, Jean B. Lasserre, Victor Magron, Edouard Pauwels

Publikováno v: Computational Optimization and Applications
Computational Optimization and Applications, 2022, 81 (1), pp.31-66. ⟨10.1007/s10589-021-00325-z⟩
Computational Optimization and Applications, Springer Verlag, 2021, ⟨10.1007/s10589-021-00325-z⟩

We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and (d+1)-th order SDP relaxations of the Moment-SOS hierarchy (dense or sparse version). With the flexible ch

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12d2bbb26cb478e7b49609cfea74b356
https://hal.laas.fr/hal-03109978

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Semi-algebraic approximation using Christoffel-Darboux kernel

Autor: Didier Henrion, Edouard Pauwels, Swann Marx, Tillmann Weisser, Jean B. Lasserre

Publikováno v: Constructive Approximation
Constructive Approximation, 2021, 54 (3), pp.391-429. ⟨10.1007/s00365-021-09535-4⟩
Constructive Approximation, Springer Verlag, 2021, 54 (3), pp.391-429. ⟨10.1007/s00365-021-09535-4⟩

International audience; We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::219ff0e236cd58484dfc1b67a5ac0eee
https://hal.science/hal-02085835v3/document

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Certifying global optimality of AC-OPF solutions via sparse polynomial optimization

Autor: Jie Wang, Victor Magron, Jean B. Lasserre

Publikováno v: Electric Power Systems Research. 213:108683

We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy -- a moment-SOS based hierarchy that exploits both correlative and term sparsity, which can provide tighter S

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64c4683d14a3620374de3dffea213eb3
https://doi.org/10.1016/j.epsr.2022.108683

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