A study of search directions in primal-dual interior-point methods for semidefinite programming

A study of search directions in primal-dual interior-point methods for semidefinite programming

We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Hae...

Semidefinite Programming : Formulations and Primal - Dual Interior - Point Methods

Parallel Primal-dual Interior-point Methods for Semidefinite Programs B-415 Parallel Primal-dual Interior-point Methods for Semidefinite Programs

The Semidefinite Program (SDP) is a fundamental problem in mathematical programming. It covers a wide range of applications, such as combinatorial optimization, control theory, polynomial optimization, and quantum chemistry. Solving extremely large-scale SDPs which could not be solved before is a significant work to open up a new vista of future applications of SDPs. Our two software packages S...

A primal-dual regularized interior-point method for semidefinite programming

Interior-point methods in semidefinite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions. Safeguards are typically required in order to handle rank-deficient Jacobians and free variables. We generalize the primal-dual regularization of Friedlander and Orban (2012) to SDP and show that it is possible to recover an optimal soluti...

A primal-dual interior point method for nonlinear semidefinite programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method.