Convergence Conditions for Variational Inequality Algorithms
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OR-282-93.pdf
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1.84 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Magnanti, Thomas L.
Perakis, Georgia
Date Issued
October 1993
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 282-93
Abstract
Within the extensive variational inequality literature, researchers have developed many algorithms. Depending upon the problem setting, these algorithms ensure the convergence of (i) the entire sequence of iterates, (ii) a subsequence of the iterates, or (iii) averages of the iterates. To establish these convergence results, the literature repeatedly invokes several basic convergence theorems. In this paper, we review these theorems and a few convergence results they imply, and introduce a new result, called the orthogonality theorem, for establishing the convergence of several algorithms for solving a certain class of variational inequalities. Several of the convergence results impose a condition of strong-f-monotonicity on the problem function. We also provide a general overview of the properties of strong-f-monotonicity, including some new results (for example, the relationship between strong-f-monotonicity and convexity).
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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