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Two Heuristic Models for Solving Generalized Nash Equilibrium Problems using a Novel Penalty Function

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dc.contributor.advisor Cojocaru, Monica
dc.contributor.advisor Thommes, Edward Fields, Roie 2021-09-08T17:30:58Z 2021-09-08T17:30:58Z 2021-09 2021-08-26
dc.description.abstract In this work, we solve Generalized Nash Equilibrium Problems using two novel heuristic models. We introduce the Shadow Point function, a novel penalty function for Generalized Nash Equilibrium Problems, similar to the Nikaido-Isoda penalty function to motivate the behavior of these two models. The first is an evolutionary-inspired algorithm which utilizes competitive selection and linear regression to motivate generation of new points. The other algorithm involves stochastic gradient descent of the Shadow Point function across mass numbers of agents to find solutions. These algorithms are evaluated on 2- and 3-player games in 2 and 3 dimensions, with both linear and non-linear shared constraints. The success of these algorithms is discussed, and the limitations of the algorithms are explored. Finally, we discuss potential remedies to these limitations, and additional ways to further optimize the methods. en_US
dc.language.iso en en_US
dc.publisher University of Guelph en_US
dc.subject Nash Games en_US
dc.subject Stochastic Gradient Descent en_US
dc.subject Evolutionary Algorithm en_US
dc.subject Generalized Nash Games en_US
dc.subject Generalized Nash Equilibrium Problems en_US
dc.subject GNEP en_US
dc.title Two Heuristic Models for Solving Generalized Nash Equilibrium Problems using a Novel Penalty Function en_US
dc.type Thesis en_US Mathematics and Statistics en_US Master of Science en_US Department of Mathematics and Statistics en_US
dc.rights.license All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated. University of Guelph en_US

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