• Corpus ID: 239024322

A New Extension of Chubanov's Method to Symmetric Cones

  title={A New Extension of Chubanov's Method to Symmetric Cones},
  author={Shingo Kanoh and Akiko Yoshise},
We propose a new variant of Chubanov’s method for solving the feasibility problem over the symmetric cone by extending Roos’s method (2018) for the feasibility problem over the nonnegative orthant. The proposed method considers a feasibility problem associated with a norm induced by the maximum eigenvalue of an element and uses a rescaling focusing on the upper bound of the sum of eigenvalues of any feasible solution to the problem. Its computational bound is (i) equivalent to Roos’s original… 


An extension of Chubanov’s algorithm to symmetric cones
This work presents an extension of Chubanov’s algorithm to the case of homogeneous feasibility problems over a symmetric cone, and uses a spectral norm that takes into account the way that K is decomposed as simple cones.
An improved version of Chubanov's method for solving a homogeneous feasibility problem
  • Kees Roos
  • Mathematics, Computer Science
    Optim. Methods Softw.
  • 2018
The Modified Main Al algorithm is in essence the same as Chubanov's Main Algorithm, except that it uses the Modified Basic Procedure as a subroutine, and it is shown that it has time complexity, just as in [1].
An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming
Chubanov's new polynomial-time algorithm for linear programming is extended to second-order cone programming based on the idea of cutting plane method and finds an -dimensional vector x which satisfies , where and is a direct product of n second- order cones and half lines.
Using Nemirovski’s Mirror-Prox method as Basic Procedure in Chubanov’s method for solving homogeneous feasibility problems
We introduce a new variant of Chubanov’s method for solving linear homogeneous systems with positive variables. In the Basic Procedure we use a recently introduced cut in combination with
Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones
A homogeneous model for standard monotone nonlinear complementarity problems over symmetric cones is proposed and the existence of a path having the following properties is shown: the path is bounded and has a trivial starting point without any regularity assumption concerning theexistence of feasible or strictly feasible solutions.
An oracle-based projection and rescaling algorithm for linear semi-infinite feasibility problems and its application to SDP and SOCP
The details are described and the polynomial complexity of the algorithm based on the real computation model proposed by Blum, Shub and Smale (the BSS model) is proved which is more suitable for floating point computation in modern computers.
Extension of primal-dual interior point algorithms to symmetric cones
Abstract. In this paper we show that the so-called commutative class of primal-dual interior point algorithms which were designed by Monteiro and Zhang for semidefinite programming extends
We consider the problem of finding nonzero vectors in full-dimensional polyhedral cones given by systems of linear inequalities. It is assumed that there is a separation oracle which, given a vector,
A Polynomial Column-wise Rescaling von Neumann Algorithm
Recently Chubanov proposed a method which solves homogeneous linear equality systems with positive variables in polynomial time. Chubanov’s method can be considered as a column-wise rescaling
A polynomial projection algorithm for linear feasibility problems
In a polynomial number of calls to the procedure the algorithm either proves that the original system is infeasible or finds a solution in the relative interior of the feasible set.