Such a problem is connected with the convex minimization problem, the complementarity problem, the problem of finding a point u ∈ E satisfying 0 = Bu and so on.
Such a problem is connected with the convex minimization problem, the complementarity problem, the problem of finding a point u ∈ C satisfying 0 ∈ Au.
Suppose furthermore that the strict complementarity of the problem (1) holds.
The absence of well defined, deep pockets in protein protein interfaces, and the large number of inter-molecular contacts arising from their high geometrical and chemical complementarity makes the problem especially difficult.
It is well-known that VEP provides a general model of several classes of problems such as the vector variational inequality, the vector complementarity problems, the vector optimization problems, the vector saddle point (minimax) problems, the multiobjective game problems, and fixed point problems (see, e.g., [2 9] and the references therein).
The generalized equilibrium problem includes, as special cases, the optimization problem, the variational inequality problem, the fixed point problem, the nonlinear complementarity, the Nash equilibrium problem in noncooperative games, the vector optimization problem, etc.
As is well known the semismooth (or smooth) Newton method is very efficient for some nonsmooth (or smooth) equations, which arise from the complementarity problem, the nonlinear programming problem, the variational inequality problem, the discretization problem of partial differential equations, the maximal monotone operator problem, etc.; see [23 25] for a detailed discussion.
The following lemma indicates the equivalence between the complementarity problem and the variational inequality problem.
The complementarity problem, the absolute value equation problem, and the related constrained optimization problem are three kinds of important optimization problems [19 23].
To solve the linear complementarity problem, the basic iteration of the active set strategies consists of two steps.
