An optimal control theory for accelerated optimization
Accelerated optimization algorithms can be generated using a double-integrator model for the search dynamics imbedded in an optimal control problem. CitationunpublishedArticleDownload View PDF
riemannian metric
Convergence to the optimal value for barrier methods combined with Hessian Riemannian gradient flows and generalized proximal algorithms
We consider the problem $\min_{x\in\R^n}\{f(x)\mid Ax=b, \ x\in\overline{C},\ g_j(x)\le0,\ j=1,\ldots,s\}$, where $b\in\R^m$, $A\in\R^{m\times n}$ is a full rank matrix, $\overline{C}$ is the closure of a nonempty, open and convex subset $C$ of $\R^n$, and $g_j(\cdot)$, $ j=1,\ldots,s$, are nonlinear convex functions. Our strategy consists firstly in to introduce a barrier-type penalty for the constraints $g_j(x)\le0$, … Read more