Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence
Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence
We study the asymptotic behavior of the solutions of evolution equations of the form $\dot u(t)\in -\partial f(u(t),r(t))$, where $f(\cdot ,r)$ is a one-parameter family of approximations of a convex function $f(\cdot )$ we wish to minimize. We investigate sufficient conditions on the parametrization $r(t)$ ensuring that the integral curves …