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PGTM with projecting in variable metric

V. G. Malinov1

AnnotationIn the work projection generalized two-step two-stage method (PGTM) with projecting in variable metric (PGTVMM) for solving finite dimensional minimization problems on the convex closed set in the Euclidean space is proposed. It may be used as well for solution of functional equations and other problems. The convergence of the method is proved for continuously differentiable convex functions with a Lipschitz gradients. Estimates rate of convergence are proved: at first linear rate of convergence for convex smooth functions, afterwards derived superlinear and quadratic rate of convergence for twice differentiable functions on supplemental suppositions.
KeywordsPGTVMM, projecting in variable metric, convergence, rate of convergence.

1Assistant Professor of Ulyanovsk State University, Ulyanovsk; vgmalinov@mail.ru.

Citation: V. G. Malinov , "[PGTM with projecting in variable metric ]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:4 (2012) 44–56 (In Russian)