The article considers a continuous extra-proximal method for equilibrium-programming problems and proves the convergence of its trajectory to one of the solutions. A regularized analogue is constructed under classical assumptions regarding errors in input data. Its convergence to the normal solution is proved.
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A. S. Antipin, “Equilibrium programming: proximal methods,” Zh. Vychisl. Mat. Mat. Fiz., 37, No. 11, 1327–1339 (1997).
A. S. Antipin, “On convergence and rate of convergence bounds of proximal methods to fixed points of extremal maps,” Zh. Vychisl. Mat. Mat. Fiz., 35, No. 5, 688–704 (1994).
A. S. Antipin, “Controlled proximal differential systems for solving saddle problems,” Diff. Uravn., 28, No. 11, 1846–1861 (1992).
F. P. Vasil’ev, Optimization Methods [in Russian], Faktorial Press, Moscow (2002).
S. V. Shpirko, Skew-Symmetric Regularization Method for Solving Equilibrium Problems [in Russian], Thesis, VTs TAN, Moscow (2000).
B. A. Budak, Continuous Methods for Solving Equilibrium-Programming Problems [in Russian], Thesis, VMiK MGU, Moscow (2003).
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Translated from Problemy Dinamicheskogo Upravleniya, Issue 4, 2009, pp. 34–56.
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Budak, B.A. Variable-Metric Continuous Proximal Methods. Comput Math Model 26, 87–106 (2015). https://doi.org/10.1007/s10598-014-9258-6
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DOI: https://doi.org/10.1007/s10598-014-9258-6