The Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach Spaces

2019 ◽  
Vol 29 (1) ◽  
pp. 767-793 ◽  
Author(s):  
C. Kanzow ◽  
V. Karl ◽  
D. Steck ◽  
D. Wachsmuth
Keyword(s):  
Nash Equilibrium ◽  
Banach Spaces ◽  
Penalty Method ◽  
Equilibrium Problems ◽  
Generalized Nash Equilibrium ◽  
Generalized Nash Equilibrium Problems

scholarly journals A note on supervised classification and Nash-equilibrium problems

2017 ◽  
Vol 51 (2) ◽  
pp. 329-341
Author(s):  
Nicolas Couellan
Keyword(s):  
Nash Equilibrium ◽  
Support Vector Machines ◽  
Supervised Classification ◽  
Dual Space ◽  
Equilibrium Problems ◽  
Support Vector ◽  
Generalized Nash Equilibrium ◽  
Class Separation ◽  
Vector Machines ◽  
Generalized Nash Equilibrium Problems

In this note, we investigate connections between supervised classification and (Generalized) Nash equilibrium problems (NEP & GNEP). For the specific case of support vector machines (SVM), we exploit the geometric properties of class separation in the dual space to formulate a non-cooperative game. NEP and Generalized NEP formulations are proposed for both binary and multi-class SVM problems.

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