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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 12, Pages 2008–2013 (Mi zvmmf9958)  

Shooting method for solving equilibrium programming problems

B. A. Budak

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

Abstract: A new iterative method is proposed for solving equilibrium programming problems. The sequence of points it generates is proved to converge weakly to the solution set of the equilibrium problem under study. If the initial point has at least one projection onto the solution set of the equilibrium problem, the sequence generated by the method is shown to converge strongly to the set of these projections. The partial gradient of the initial data is assumed to be invertible and strictly monotone, which differs from the classical skew-symmetry condition.

Key words: equilibrium programming, invertible and strictly monotone gradient, shooting method, strong convergence, weak convergence, skew-symmetry.

DOI: https://doi.org/10.7868/S0044466913120041

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:12, 1819–1824

Bibliographic databases:

Document Type: Article
UDC: 519.626
Received: 01.07.2013

Citation: B. A. Budak, “Shooting method for solving equilibrium programming problems”, Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013), 2008–2013; Comput. Math. Math. Phys., 53:12 (2013), 1819–1824

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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