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 M_{j} (resp. A_{j}) which are rigid, i.e. unique up to conjugacy once the classes C_{j} (resp. c_{j}) are fixed. For rigid representations the sum of the dimensions of the classes C_{j} (resp. c_{j}) equals 2n^{2}-2.