A conical algorithm for solving a class of complementarity problems. (English) Zbl 0618.90090

Tuy, Hoang

Acta Math. Vietnam. 6, No. 1, 3-17 (1981).

The concave complementarity problem: \(x\geq 0\), \(y=w(x)\geq 0\), \(x^ Ty=0\) \((x\in R^ n\), \(y\in R^ n\), \(w: R^ n\to R^ n\) a concave mapping) is converted into a concave minimization problem under convex constraints and solved by a conical algorithm for concave minimization. A special feature of this concave minimization problem is that its optimal value is equal to zero. This feature is exploited to devise simpler rules for bounding and fathoming than in the general concave minimization problem. The method solves the problem whenever it is solvable.

MSC:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K05	Numerical mathematical programming methods
49M37	Numerical methods based on nonlinear programming
90C30	Nonlinear programming

Keywords:

concave complementarity problem; concave minimization; convex constraints; conical algorithm