Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming

Primal-dual path-following algorithms for circular programming

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

New complexity analysis of a full Nesterov-Todd steps IIPM for semidefinite optimization

Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions

In this paper we study primal-dual path-following algorithms for the second-order cone programming (SOCP) based on a family of directions that is a natural extension of the Monteiro-Zhang (MZ) family for semidefinite programming. We show that the polynomial iteration-complexity bounds of two well-known algorithms for linear programming, namely the short-step path-following algorithm of Kojima e...

A Recurrent Neural Network Model for Solving Linear Semidefinite Programming

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

Primal-Dual Path-Following Algorithms for Semidefinite Programming

This paper deals with a class of primal-dual interior-point algorithms for semideenite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara 11]. These authors proposed a family of primal-dual search directions that generalizes the one used in algorithms for linear programming based on the scaling matrix X 1=2 S ?1=2. They study three primal-dual algorithms based on this f...

Primal-dual path-following algorithms for circular programming

Circular programming problems are a new class of convex optimization problems in which we minimize linear function over the intersection of an affine linear manifold with the Cartesian product of circular cones. It has very recently been discovered that, unlike what has previously been believed, circular programming is a special case of symmetric programming, where it lies between second-order ...