An optimal variant of Kelley’s cutting-plane method

An Analyti Center Cutting Plane Method

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...

A Homogenized Cutting Plane Method

Analytic Center Cutting-Plane Method

The Complexity of the Cutting Plane Method

The cutting plane method solves a linear relaxation of the problem obtained by dropping the integrality constraint. Given an integer programming problem, it proceeds as follows: If the optimum solution found is not integral, then a cut inequality separating the optimum from all integer solutions is added to the LP and the LP is solved again; this two-step procedure is repeated till an integral ...