Solving large structured semidefinite programs using an inexact spectral bundle method

Semidefinite programs have received a great deal of attention because of the variety of problems that they can model and the rich theory that leads to polynomial-time algorithms to solve them. However, large practical problems are still hard to solve because most algorithms ignore the structure of the problem. We present an algorithm for solving semidefinite programs that exploits structure yet is not tailored a priori to any particular structure. It adapts a bundle method designed to solve structured LMI feasibility problems. Duality provides a tight lower bound for the optimal cost for use in a termination criterion. A numerical experiment demonstrates that the complexity is comparable to that of structured interior-point methods, and unlike those methods it applies to a general class of structures.