Here, we show that this condition metric induces a Lipschitz Riemannian structure on that space. After investigating geodesics in such a nonsmooth structure, we ...

Oct 30, 2009 · Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating geodesics in such a nonsmooth ...

Using nons- mooth analysis techniques, we prove that any condition geodesic is C1 with a locally Lipschitz derivative (Theorem 2). Such techniques are already ...

This paper is dedicated to Steve Smale, on his 80th birthday. Abstract. In our previous paper [2], we studied the condition metric in the space of maximal.

When this smallest singular value has multiplicity 1, the function A → log ⁡ ( σ n ( A ) − 2 ) is a convex function with respect to the condition Riemannian ...

Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating geodesics in such a nonsmooth structure, we ...

It is proved that $\alpha$ is self-convex when restricted to the largest open set of points $x$ where there is a unique closest point in $\mathcal{N}$ to ...

In the present paper, we introduce the generalized geodesic convex functions on Riemannian manifolds and present some of their properties. Based on these ...

Jan 1, 2012 · Here, we show that this condition metric induces a Lipschitz Riemannian structure on that space. After investigating geodesics in such a ...

Abstract: In our previous paper [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1491-1506], we studied the condition metric in the space of maximal rank n × m ...