Volume 26, Number 3, 2000
PERTURBED PROXIMAL POINT ALGORITHM WITH NONQUADRATIC KERNEL
M. Brohe,
M.Brohe@ulg.ac.be ,
P. Tossings
Patricia.Tossings@ulg.ac.be
2000 Mathematics Subject Classification: 47H04, 47H05, 47H09, 47H10. Key words: Proximal point algorithm, Bregman functions, generalized resolvent operator, variational convergence.
A well-known algorithm, developed by R. T. Rockafellar [16],
for solving the problem
(P)
``To find [`x] Î H such that 0
Î T[`x]''
is the proximal point algorithm.
Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization,...
We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.
A RECESSION NOTION FOR A CLASS OF MONOTONE BIVARIATE FUNCTIONS
A. Moudafi
amoudafi@martinique.univ-ag.fr
2000 Mathematics Subject Classification: 49M45, 49M10, 65K10, 90C25. Key words: Bivariate function, recession notion, Yosida approximate, variational convergence, convex optimization, maximal monotone operators.
COMPLETE SYSTEMS OF HERMITE ASSOCIATED FUNCTIONS
Peter Rusev
pkrusev@math.bas.bg
2000 Mathematics Subject Classification: 30B60, 33C45. Key words: Hermite polynomials, Hermite associated functions, completeness.
DIFFERENTIAL EQUATIONS IN ABSTRACT CONES
Tadeusz Jankowski
tjank@mif.pg.gda.pl
2000 Mathematics Subject Classification: 34A45, 34K99. Key words: Quasilinearization, monotone iterations, superlinear and semi--superlinear convergence.
A CHARACTERIZATION OF VARIETIES OF ASSOCIATIVE ALGEBRAS OF EXPONENT TWO
A. Giambruno
a.giambruno@unipa.it,
M. Zaicev
zaicev@mech.math.msu.su
2000 Mathematics Subject Classification: Primary 16R10, 16P90. Key words: variety of algebras, polynomial identity.
SOME EXAMPLES OF RIGID REPRESENTATION
Vladimir Petrov Kostov
kostov@math.unice.fr
2000 Mathematics Subject Classification: 15A24. Key words: monodromy group, rigid representation.
We give new examples of existence of such (p+1)-tuples of matrices Mj (resp. Aj) which are rigid, i.e. unique up to conjugacy once the classes Cj (resp. cj) are fixed. For rigid representations the sum of the dimensions of the classes Cj (resp. cj) equals 2n2-2.