Solving nonlinear multicommodity flow problems by the analytic center cutting plane method

Solving nonlinear multicommodity flow problems by the analytic center cutting plane method

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a...

Solving Nonlinear Multicommodity Flow Problems by the Proximal Chebychev Center Cutting Plane Algorithm

The recent algorithm proposed in [15] (called pcpa) for convex nonsmooth optimization, is specialized for applications in telecommunications on some nonlinear multicommodity flows problems. In this context, the objective function is additive and this property could be exploited for a better performance.

Analytic Center Cutting-Plane Method

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 ...

An Analytic Center Cutting Plane Method for Semidefinite Feasibility Problems

Semidefinite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as finding a point in a nonempty bounded convex body Γ in the cone of symmetric positive semidefinite matrices. Assume that Γ is defined by an oracle, which for any given m ×m symmetric positive semidefinite matrix Ŷ either confirms that Ŷ ∈ Γ or returns a cut, i.e....