A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming

Abstract EN

When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration.

For problems of large size, solving the system of linear equations can be very expensive.

In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems.

At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations.

Under mild assumptions, the convergence of this algorithm is established.

Numerical examples are given to illustrate the convergence results obtained.