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On the convergence of descent methods for monotone variational inequalities. (English) Zbl 0828.90127
Recently, Zhu and Marcotte (1993) established the convergence of a modified descent algorithm for monotone variational inequalities. Using algorithmic equivalence results due to Patriksson (1993) and Larsson and Patriksson (1994), we show that this convergence result may be used to establish the convergence of slightly modified versions of the classical successive approximation algorithms of Dafermos (1983) and Cohen (1988), and of the descent algorithms of Wu, Florian and Marcotte (1993), Patriksson (1993), and Larsson and Patriksson (1994), under assumptions that are both much milder and much easier to verify than those for their original statements.

90C30 Nonlinear programming
49J40 Variational inequalities
Full Text: DOI
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