Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Computing generalized Nash equilibria by polynomial programming
AU - Couzoudis, Eleftherios
AU - Renner, Philipp
PY - 2013/6
Y1 - 2013/6
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 -