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Zbl 1039.90529
Auslender, Alfred; Teboulle, Marc; Ben-Tiba, Sami
A logarithmic-quadratic proximal method for variational inequalities. (English)
[J] Comput. Optim. Appl. 12, No. 1-3, 31-40 (1999). ISSN 0926-6003; ISSN 1573-2894/e

Summary: We present a new method for solving variational inequalities on polyhedra. The method is proximal based, but uses a very special logarithmic-quadratic proximal term which replaces the usual quadratic, and leads to an interior proximal type algorithm. We allow for computing the iterates approximately and prove that the resulting method is globally convergent under the sole assumption that the optimal set of the variational inequality is nonempty.

MSC 2000:: *90C33 Complementarity problems
49J40 Variational methods including variational inequalities
65K05 Mathematical programming (numerical methods)
90C51 Interior-point methods

Keywords: variational inequalities; nonlinear complementarity; proximal-like methods; maximal monotone operators; global convergence; interior point methods; saddle point computation

Cited in: Zbl 1260.47069 Zbl 1155.65054 Zbl 1105.49013 Zbl 1104.90049 Zbl 1039.90053

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