# Minimizing Condition Number via Convex Programming

@article{Lu2011MinimizingCN, title={Minimizing Condition Number via Convex Programming}, author={Zhaosong Lu and Ting Kei Pong}, journal={SIAM J. Matrix Anal. Appl.}, year={2011}, volume={32}, pages={1193-1211} }

In this paper we consider minimizing the spectral condition number of a positive semidefinite matrix over a nonempty closed convex set $\Omega$. We show that it can be solved as a convex programming problem, and moreover, the optimal value of the latter problem is achievable. As a consequence, when $\Omega$ is positive semidefinite representable, it can be cast into a semidefinite programming problem. We then propose a first-order method to solve the convex programming problem. The…

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