Projection generalized two-point extragradient quasi-Newton method for saddle-point and other problems.

*(English. Russian original)*Zbl 1450.65050
Comput. Math. Math. Phys. 60, No. 2, 227-239 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 2, 221-233 (2020).

Summary: A method for solving saddle-point and other problems is proposed whereby saddle points are found for a convex-concave continuously differentiable function with Lipschitz partial gradients defined on a convex closed subset of Euclidean space. The convergence of the method and its convergence rate estimate are proved using convex analysis tools without assuming that the function is strongly convex-concave.

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\textit{V. G. Malinov}, Comput. Math. Math. Phys. 60, No. 2, 227--239 (2020; Zbl 1450.65050); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 2, 221--233 (2020)

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