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**Computing generalized Nash equilibria by polynomial programming.** / Couzoudis, Eleftherios; Renner, Philipp.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Couzoudis, E & Renner, P 2013, 'Computing generalized Nash equilibria by polynomial programming', *Mathematical Methods of Operational Research*, vol. 77, no. 3, pp. 459-472. https://doi.org/10.1007/s00186-012-0422-5

Couzoudis, E., & Renner, P. (2013). Computing generalized Nash equilibria by polynomial programming. *Mathematical Methods of Operational Research*, *77*(3), 459-472. https://doi.org/10.1007/s00186-012-0422-5

Couzoudis E, Renner P. Computing generalized Nash equilibria by polynomial programming. Mathematical Methods of Operational Research. 2013 Jun;77(3):459-472. Epub 2013 Jan 3. doi: 10.1007/s00186-012-0422-5

@article{eb3711f6d4d247a1af5d14291f5d06eb,

title = "Computing generalized Nash equilibria by polynomial programming",

abstract = "We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar{\textquoteright}s Positivstellensatz, a representation result for positive polynomials, to replace each agent{\textquoteright}s problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.",

keywords = "Generalized nash equilibrium , Parametrized optimization , Real algebraic geometry, Nonconvex optimization, Electricity spot market, Transmission loss ",

author = "Eleftherios Couzoudis and Philipp Renner",

year = "2013",

month = jun,

doi = "10.1007/s00186-012-0422-5",

language = "English",

volume = "77",

pages = "459--472",

journal = "Mathematical Methods of Operational Research",

issn = "1432-2994",

publisher = "Physica-Verlag",

number = "3",

}

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T1 - Computing generalized Nash equilibria by polynomial programming

AU - Couzoudis, Eleftherios

AU - Renner, Philipp

PY - 2013/6

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N2 - We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar’s Positivstellensatz, a representation result for positive polynomials, to replace each agent’s problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.

AB - We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar’s Positivstellensatz, a representation result for positive polynomials, to replace each agent’s problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.

KW - Generalized nash equilibrium

KW - Parametrized optimization

KW - Real algebraic geometry

KW - Nonconvex optimization

KW - Electricity spot market

KW - Transmission loss

U2 - 10.1007/s00186-012-0422-5

DO - 10.1007/s00186-012-0422-5

M3 - Journal article

VL - 77

SP - 459

EP - 472

JO - Mathematical Methods of Operational Research

JF - Mathematical Methods of Operational Research

SN - 1432-2994

IS - 3

ER -