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| Volume 2, Number 3, September 2006, pp. 679-692 | |||||||||
| J.S. Pang and J. Sun | |||||||||
| Key words: | |||||||||
| piecewise quadratic program, Nash equilibria, sequential penalization | |||||||||
| Mathematices Subject Classification: 90C20, 91A06, 91B50 | |||||||||
|
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| Volume 2, Number 3, September 2006, pp. 679-692 | |||||||||
| J.S. Pang and J. Sun | |||||||||
| Key words: | |||||||||
| piecewise quadratic program, Nash equilibria, sequential penalization | |||||||||
| Mathematices Subject Classification: 90C20, 91A06, 91B50 | |||||||||
|
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| Abstract: | |||
| Inspired by an applied model arising from electric power markets with price caps that is discussed in a previous paper [3], this paper studies the Nash equilibrium problem in which the minimizing players' objective functions are sums of composite separable convex piecewise quadratic functions. Based on a fundamental but previously not proven equivalence between a separable convex piecewise quadratic program and a standard convex quadratic program, we show that the nonsmooth Nash equilibrium problem can be equivalently reformulated as a generalized Nash equilibrium problem with coupled linear constraints. We establish the convergence of a sequential penalized Nash algorithm for solving the reformulated generalized Nash problem under a boundedness condition. | |||
| Nash equilibria with piecewise quadratic osts | ||