Theoretical challenges towards cutting-plane selection

Towards a Practical Volumetric Cutting Plane Method for Convex Programming

We consider the volumetric cutting plane method for nding a point in a convex set C < n that is characterized by a separation oracle. We prove polynomiality of the algorithm with each added cut placed directly through the current point, and show that this \central cut" version of the method can be implemented using no more than 25n constraints at any time. with support from a CORE fellowship.

Cutting Plane Algorithms for Integer Programming, Cutting Plane Algorithms

Cutting plane methods are exact algorithms for integer programming problems. They have proven to be very useful computationally in the last few years, especially when combined with a branch and bound algorithm in a branch and cut framework. These methods work by solving a sequence of linear programming relax-ations of the integer programming problem. The relaxations are gradually improved to gi...

Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutti...

A Homogenized Cutting Plane Method

Data Compression of Cutting Plane

We propose an efficient algorithm for compressing cutting plane of three dimensional Computational Fluid Dynamics (CFD) data set. Observing the cutting planes of large 3D CFD data set is an important method for examination of simulation result, and efficient compression algorithm of these cutting planes is important for good performance of visualization when the simulation is running in a remot...