A Convex Programming Approach to Solve Posynomial Systems

Marianne Akian; Xavier Allamigeon; Marin Boyet; Stéphane Gaubert

doi:10.1007/978-3-030-52200-1_24

A Convex Programming Approach to Solve Posynomial Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This extends the convex programming approach of one player stochastic games.

Original language	English
Title of host publication	Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings
Editors	Anna Maria Bigatti, Jacques Carette, James H. Davenport, Michael Joswig, Timo de Wolff
Publisher	Springer
Pages	241-250
Number of pages	10
ISBN (Print)	9783030521998
DOIs	https://doi.org/10.1007/978-3-030-52200-1_24
Publication status	Published - 1 Jan 2020
Event	7th International Congress on Mathematical Software, ICMS 2020 - Braunschweig, Germany Duration: 13 Jul 2020 → 16 Jul 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12097 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Congress on Mathematical Software, ICMS 2020
Country/Territory	Germany
City	Braunschweig
Period	13/07/20 → 16/07/20

Access to Document

10.1007/978-3-030-52200-1_24

Cite this

Akian, M., Allamigeon, X., Boyet, M., & Gaubert, S. (2020). A Convex Programming Approach to Solve Posynomial Systems. In A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig, & T. de Wolff (Eds.), Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings (pp. 241-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12097 LNCS). Springer. https://doi.org/10.1007/978-3-030-52200-1_24

Akian, Marianne ; Allamigeon, Xavier ; Boyet, Marin et al. / A Convex Programming Approach to Solve Posynomial Systems. Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings. editor / Anna Maria Bigatti ; Jacques Carette ; James H. Davenport ; Michael Joswig ; Timo de Wolff. Springer, 2020. pp. 241-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A Convex Programming Approach to Solve Posynomial Systems",

abstract = "We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This extends the convex programming approach of one player stochastic games.",

author = "Marianne Akian and Xavier Allamigeon and Marin Boyet and St{\'e}phane Gaubert",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 7th International Congress on Mathematical Software, ICMS 2020 ; Conference date: 13-07-2020 Through 16-07-2020",

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doi = "10.1007/978-3-030-52200-1\_24",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Akian, M , Allamigeon, X, Boyet, M & Gaubert, S 2020, A Convex Programming Approach to Solve Posynomial Systems. in AM Bigatti, J Carette, JH Davenport, M Joswig & T de Wolff (eds), Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12097 LNCS, Springer, pp. 241-250, 7th International Congress on Mathematical Software, ICMS 2020, Braunschweig, Germany, 13/07/20. https://doi.org/10.1007/978-3-030-52200-1_24

A Convex Programming Approach to Solve Posynomial Systems. / Akian, Marianne ; Allamigeon, Xavier; Boyet, Marin et al.
Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings. ed. / Anna Maria Bigatti; Jacques Carette; James H. Davenport; Michael Joswig; Timo de Wolff. Springer, 2020. p. 241-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12097 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - A Convex Programming Approach to Solve Posynomial Systems

AU - Akian, Marianne

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AU - Boyet, Marin

AU - Gaubert, Stéphane

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N2 - We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This extends the convex programming approach of one player stochastic games.

AB - We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This extends the convex programming approach of one player stochastic games.

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DO - 10.1007/978-3-030-52200-1_24

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SN - 9783030521998

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings

A2 - Bigatti, Anna Maria

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A2 - Davenport, James H.

A2 - Joswig, Michael

A2 - de Wolff, Timo

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T2 - 7th International Congress on Mathematical Software, ICMS 2020

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Akian M , Allamigeon X, Boyet M, Gaubert S. A Convex Programming Approach to Solve Posynomial Systems. In Bigatti AM, Carette J, Davenport JH, Joswig M, de Wolff T, editors, Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings. Springer. 2020. p. 241-250. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-52200-1_24

A Convex Programming Approach to Solve Posynomial Systems

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