Convergence of a subgradient method for computing the bound norm of matrices (Q1057619)

For a linear map \(A: R^ n\to R^ m\), where \(R^ n\) and \(R^ m\) are endowed with norms \(\psi\) and \(\phi\), the bound norm is defined by \(S_{\phi \psi}(A)=\sup \{\phi (Ax):\psi (x)\leq 1\}.\) A subgradient method for computing \(S_{\phi \psi}\) is given and it is shown that it converges if \(\phi\) or \(\psi\) are polyhedral. The paper is written in French.