Abstract:
In 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.
Keywords:PGTVMM, projecting in variable
metric, convergence, rate of convergence.
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