Modified descent methods for solving monotone variational inequalities (1993) [3 citations — 2 self]
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by D. L. Zhu, P. Marcotte
Operations Research Letters
http://www.iro.umontreal.ca/~marcotte/ARTIPS/orl.ps.gz
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Abstract:
Recently, Fukushima proposed a differentiable optimization framework for solving strictly monotone and continuously differentiable variational inequalities. The main result of this paper is to show that Fukushima's results can be extended to monotone (not necessarily strictly monotone) and Lipschitz continuous (not necessarily continuously differentiable) variational inequalities, if one is willing to modify slightly the basic algorithmic scheme. The modification
Citations
| 64 | Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems – Fukushima - 1992 |
| 61 | An iterative method of solving a game – Robinson - 1951 |
| 25 | Iterative methods for variational and complementarity problems – Pang, Chan - 1982 |
| 15 | A new algorithm for solving variational inequalities with application to the traffic assignment problem – Marcotte - 1985 |
| 6 | On some nonlinear elliptic differential functional equations – Hartman, Stampacchia - 1966 |
| 5 | An extended descent framework for monotone variational inequalities – Zhu, Marcotte - 1994 |
| 4 | Modification of the extragradient method for solving variational inequalities and certain optimization problems – Khobotov - 1987 |
| 4 | Nonlinear Programming: A Unified Approach (Prentice-Hall – Zangwill - 1969 |
