My Ph.D. thesis was on the matrix nearness problems arising in control theory. The major problems that I tackled in my thesis were
There are two aspects of the thesis. Some parts of the thesis is on the derivation of singular value optimization characterizations, for which the basic tool that I depend on is the perturbation theory of eigenvalues and singular values. Some effort is also spent on the analysis of the optimal points (specifically see the chapter on the pseudosectral radius) for the singular value optimization problems. The rest of the thesis is computational. Typically for each singular value optimization problem fast algorithms are introduced. The convergence properties of these algorithms as well as their accuracy are analyzed in detail.