An analytic center cutting plane algorithm for finding equilibrium points

An analytic center cutting plane algorithm for finding equilibrium points

We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyz...

An Analytic Center Cutting Plane Method

Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which, for any given m m symmetric matrix ^ Y , either connrms that ^ Y 2 ? or returns a cut, i.e., a symmetric matrix A...

Analytic Center Cutting-Plane Method

An analytic center cutting plane method for pseudomonotone variational inequalities

We consider an analytic center algorithm for solving generalized monotone variational inequalities in R", which adapts a recent result due to Goffin et al. (1993) to the numerical resolution of continuous pseudomonotone variational inequalities.

An Analytic Center Cutting Plane Method for Semideenite Feasibility Problems

Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which for any given m m symmetric positive semideenite matrix ^ Y either connrms that ^ Y 2 ? or returns a cut, i.e., a ...