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On some methods of descent over groups of variables. (English. Russian original) Zbl 0842.65043
J. Math. Sci., New York 74, No. 5, 1219-1224 (1995); translation from Issled. Prikl. Mat. 19, 24-33 (1992).
This paper is devoted to the study of the convergence of certain methods for unconstrained optimization belonging to a class of decomposition methods of nonlinear programming. The methods of this class are characterized by the property that at each step the transition from one point to another is carried out not over all the variables of the problem, but only over a group of variables. The ideas of descent over groups of variables are implicit, for example in the methods of coordinatewise descent, gradient descent over fast and slow variables, and others. We give sufficient conditions for convergence of methods of this type.
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
Full Text: DOI
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