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Semi-smooth Newton methods for the Signorini problem

Kazufumi Ito, Karl Kunisch (2008)

Applications of Mathematics

Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.

Some convergence acceleration processes for a class of vector sequences

G. Sedogbo (1997)

Applicationes Mathematicae

Let ( S n ) be some vector sequence, converging to S, satisfying S n - S ∼ ϱ n n θ ( β 0 + β 1 n - 1 + β 2 n - 2 + . . . ) , 0 | ϱ | 1 , θ 0 , where β 0 ( ≠ 0 ) , β 1 , . . . are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.

Some notes on the quasi-Newton methods

Masanori Ozawa, Hiroshi Yanai (1982)

Aplikace matematiky

A survey note whose aim is to establish the heuristics and natural relations in a class of Quasi-Newton methods in optimization problems. It is shown that a particular algorithm of the class is specified by characcterizing some parameters (scalars and matrices) in a general solution of a matrix equation.

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