1982
DOI: 10.1007/bf01585112
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Iterative methods for variational and complementarity problems

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Cited by 265 publications
(83 citation statements)
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“…summarizes the traffic in the network as generated by the users and the parameters k i of the user objective. The user traffic rates are coupled through the constraint of the form N i=1 A li x i ≤ C l for all l ∈ L , where C l is the maximum aggregate traffic through link l. The constraint can be compactly written as Ax ≤ C, where C is the link capacity vector and is given by C = (10,15,20,10,15,20,20,15,25).…”
Section: A Regularized Dualmentioning
confidence: 99%
See 1 more Smart Citation
“…summarizes the traffic in the network as generated by the users and the parameters k i of the user objective. The user traffic rates are coupled through the constraint of the form N i=1 A li x i ≤ C l for all l ∈ L , where C l is the maximum aggregate traffic through link l. The constraint can be compactly written as Ax ≤ C, where C is the link capacity vector and is given by C = (10,15,20,10,15,20,20,15,25).…”
Section: A Regularized Dualmentioning
confidence: 99%
“…Related is also the literature on centralized projection-based methods for optimization (see for example books [3,8,21]) and variational inequalities [8,[10][11][12]20,24]. Recently, efficient projection-based algorithms have been developed in [1,2,18,26] for optimization, and in [17,19] for variational inequalities.…”
mentioning
confidence: 99%
“…We leave the issue of computing x(t) and z(t) open (see [2,5,20,32] Hence, by the definition of c and 0, :ll(t)ll 2 > I$I(t+l)1 2 -c(t) 2 -11Ax(t)11 2 + 2c(t)cFllx(t)11 2 + c(t) 2 11BA(t)ll 2 > lI(t+1)112 + c(t)(2a-c(t)p(ATA))Il2(t)112 + c(t) 2 11B2(t)11 2 .…”
Section: Application To Variational Inequalitiesmentioning
confidence: 99%
“…where M is the minimum cost of travel between o and n. Alternately, a diagonalisation algorithm referred to as the nonlinear Jacobi method has been used by many authors including Abduaal and LeBlanc (1979), Ahn (1979), Florian and Spiess (1982), Dafermos (1982), and Pang and Chan (1982) among others. In a diagonalisation algorithm, at each iteration n, diagonalisation is performed such that all the flows on links other than the flow on current link, v are fixed.…”
Section: Satisfaction Of Conditions For Good Behaviourmentioning
confidence: 99%