On the Convergence of Descent Methods for Monotone Variational Inequalities

Michael Patriksson
Department of Mathematics
Linköping Institute of Technology
Linköping
Sweden

ABSTRACT:

Recently, Zhu and Marcotte (1993) established the convergence of a
modified descent algorithm for monotone variational inequalities.
Using algorithmic equivalence results due to Patriksson (1993a, 1993b)
and Larsson and Patriksson (1990), we show that this convergence
result may be used to establish the convergence of slightly modified
versions of the classical successive approximat ion algorithms of
Dafermos (1983) and Cohen (1988), and of the descent algorithms of Wu
et al. (1990), Patriksson (1993a, 1993b), and Larsson and Patriksson
(1990), under assumptions that are both much milder and much easier to
verify than those for their original statements.

KEY WORDS: Monotone Variational Inequalities, Successive Approximation
Algorithms, Merit Functions, Descent Methods, Algorithmic Equivalence,
Convergence