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A new inexact alternating directions method for monotone variational inequalities. (English) Zbl 1009.90108
Given real matrices A of order l×n and B of order l×m, let Ω={(x,y)|xX,yY,Ax+By=b} where X and Y are given nonempty closed convex subsets of n and m , respectively, and b is a given vector in m · Let F(u)=f(x)g(y), where f:X n and g:Y m are given monotone operators. This paper studies the variational inequality problem of determining a vector u * Ω such that (u-u * ) T F(u * )0 for all uΩ· An inexact alternating directions method for the above problem is presented that extends the method given in J. Eckstein, “Some saddle-function splitting methods for convex programming”, Optim. Methods Software 4, 75-83 (1994)].

MSC:
90C30Nonlinear programming
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
65K05Mathematical programming (numerical methods)