On the Nesterov--Todd Direction in Semidefinite Programming

On the Nesterov-Todd Direction in Semidefinite Programming

We study different choices of search direction for primal-dual interior-point methods for semidefinite programming problems. One particular choice we consider comes from a specialization of a class of algorithms developed by Nesterov and Todd for certain convex programming problems. We discuss how the search directions for the Nesterov-Todd (NT) method can be computed efficiently and demonstrat...

An Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Programming

This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd step for semidefinite programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). The polynomial bound coincides with that of infeasible interior-point methods for linear programming, namely, O(n log n/ε).

New Complexity Analysis of a Full Nesterov-todd Steps Iipm for Semidefinite Optimization

In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obt...

Nesterov-Todd Directions are Newton Directions

The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. The standard search directions for interior-point methods applied to self-scaled conic programming problems are the so-called Nesterov-Todd directions. In this article we show that these direct...

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