2 Search Results for "Tsigaridas, Elias"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.79
A Faster Interior-Point Method for Sum-Of-Squares Optimization

Authors: Shunhua Jiang, Bento Natura, and Omri Weinstein

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let p = ∑_i q²_i be an n-variate SOS polynomial of degree 2d. Denoting by L : = binom(n+d,d) and U : = binom(n+2d,2d) the dimensions of the vector spaces in which q_i’s and p live respectively, our algorithm runs in time Õ(LU^{1.87}). This is polynomially faster than state-of-art SOS and semidefinite programming solvers [Jiang et al., 2020; Huang et al., 2021; Papp and Yildiz, 2019], which achieve runtime Õ(L^{0.5} min{U^{2.37}, L^{4.24}}). The centerpiece of our algorithm is a dynamic data structure for maintaining the inverse of the Hessian of the SOS barrier function under the polynomial interpolant basis [Papp and Yildiz, 2019], which efficiently extends to multivariate SOS optimization, and requires maintaining spectral approximations to low-rank perturbations of elementwise (Hadamard) products. This is the main challenge and departure from recent IPM breakthroughs using inverse-maintenance, where low-rank updates to the slack matrix readily imply the same for the Hessian matrix.
Cite as

Shunhua Jiang, Bento Natura, and Omri Weinstein. A Faster Interior-Point Method for Sum-Of-Squares Optimization. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 79:1-79:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{jiang_et_al:LIPIcs.ICALP.2022.79,
  author =	{Jiang, Shunhua and Natura, Bento and Weinstein, Omri},
  title =	{{A Faster Interior-Point Method for Sum-Of-Squares Optimization}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{79:1--79:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.79},
  URN =		{urn:nbn:de:0030-drops-164205},
  doi =		{10.4230/LIPIcs.ICALP.2022.79},
  annote =	{Keywords: Interior Point Methods, Sum-of-squares Optimization, Dynamic Matrix Inverse}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.21
Geometric Algorithms for Sampling the Flux Space of Metabolic Networks

Authors: Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas, and Haris Zafeiropoulos

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
Systems Biology is a fundamental field and paradigm that introduces a new era in Biology. The crux of its functionality and usefulness relies on metabolic networks that model the reactions occurring inside an organism and provide the means to understand the underlying mechanisms that govern biological systems. Even more, metabolic networks have a broader impact that ranges from resolution of ecosystems to personalized medicine. The analysis of metabolic networks is a computational geometry oriented field as one of the main operations they depend on is sampling uniformly points from polytopes; the latter provides a representation of the steady states of the metabolic networks. However, the polytopes that result from biological data are of very high dimension (to the order of thousands) and in most, if not all, the cases are considerably skinny. Therefore, to perform uniform random sampling efficiently in this setting, we need a novel algorithmic and computational framework specially tailored for the properties of metabolic networks. We present a complete software framework to handle sampling in metabolic networks. Its backbone is a Multiphase Monte Carlo Sampling (MMCS) algorithm that unifies rounding and sampling in one pass, obtaining both upon termination. It exploits an improved variant of the Billiard Walk that enjoys faster arithmetic complexity per step. We demonstrate the efficiency of our approach by performing extensive experiments on various metabolic networks. Notably, sampling on the most complicated human metabolic network accessible today, Recon3D, corresponding to a polytope of dimension 5335, took less than 30 hours. To our knowledge, that is out of reach for existing software.
Cite as

Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas, and Haris Zafeiropoulos. Geometric Algorithms for Sampling the Flux Space of Metabolic Networks. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{chalkis_et_al:LIPIcs.SoCG.2021.21,
  author =	{Chalkis, Apostolos and Fisikopoulos, Vissarion and Tsigaridas, Elias and Zafeiropoulos, Haris},
  title =	{{Geometric Algorithms for Sampling the Flux Space of Metabolic Networks}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.21},
  URN =		{urn:nbn:de:0030-drops-138201},
  doi =		{10.4230/LIPIcs.SoCG.2021.21},
  annote =	{Keywords: Flux analysis, metabolic networks, convex polytopes, random walks, sampling}
}
  • Refine by Author
  • 1 Chalkis, Apostolos
  • 1 Fisikopoulos, Vissarion
  • 1 Jiang, Shunhua
  • 1 Natura, Bento
  • 1 Tsigaridas, Elias
  • Show More...

  • Refine by Classification
  • 1 Applied computing → Systems biology
  • 1 Computing methodologies → Modeling and simulation
  • 1 Mathematics of computing → Continuous functions
  • 1 Mathematics of computing → Convex optimization
  • 1 Mathematics of computing → Mathematical software
  • Show More...

  • Refine by Keyword
  • 1 Dynamic Matrix Inverse
  • 1 Flux analysis
  • 1 Interior Point Methods
  • 1 Sum-of-squares Optimization
  • 1 convex polytopes
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2021
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact