A second-order cone cutting surface method: complexity and application

We present an analytic center cutting surface algorithm that uses mixed linear and multiple second-order cone cuts. Theoretical issues and applications of this technique are discussed. From the theoretical viewpoint, we derive two complexity results. We show that an approximate analytic center can be recovered after simultaneously adding $p$ second-order cone cuts in $O(p\log(p+1))$ Newton … Read more

A matrix generation approach for eigenvalue optimization

We study the extension of a column generation technique to eigenvalue optimization. In our approach we utilize the method of analytic center to obtain the query points at each iteration. A restricted master problem in the primal space is formed corresponding to the relaxed dual problem. At each step of the algorithm, an oracle is … Read more

An interior point cutting plane method for convex feasibility problem with second-order cone inequalities

Convex feasibility problem in general, is a problem of finding a point in a convex set contains a full dimensional ball and is contained in a compact convex set. We assume that the outer set is described by second-order cone inequalities and propose an analytic center cutting plane technique to solve this problem. We discuss … Read more