Some methods based on the D-gap function for solving monotone variational inequalities. (English) Zbl 1168.49303

Solodov, Michael V.; Tseng, Paul

Comput. Optim. Appl. 17, No. 2-3, 255-277 (2000).

Summary: The D-gap function has been useful in developing unconstrained descent methods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for monotone variational inequality problems with bounded feasible set. Accordingly, we develop two unconstrained methods based on them that are similar in spirit to a feasible method of Zhu and Marcotte based on the regularized-gap function. We further discuss a third method based on applying the D-gap function to a regularized problem. Preliminary numerical experience is also reported.

MSC:

49J40	Variational inequalities
49K40	Sensitivity, stability, well-posedness
90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

monotone variational inequalities; implicit Lagrangian; D-gap function; stationary point; descent methods

Software:

QPCOMP