AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
TL;DR
Theoretical analysis confirms that these inexact variants of GRPDA retain the convergence properties of their exact counterparts, and they are applied to some total-variation-based image deblurring problems.
We analyze an inexact, proximal trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. Our algorithm leverages the proximal gradient as a benchmark to guarantee global convergence. However, evaluating the proximal gradient involves solving a nonsmooth convex optimi...
We consider nonconvex conic optimization that covers Standard Nonlinear Programming, Semidefinite Programming, Second Order Cone Programming. To the dual Lagrangian problem, we associate a relaxed primal convex problem, and give bounds for the duality gap. Then we propose a proximal extension of the column generation m...
A new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian that achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual, the first second-order method for this problem class attaining this rate.
This work proposes an inexact primal-dual Newton method with an inner solver based on the conjugate residual (CR) method, which handles indefiniteness in the subproblem directly as it arises and establishes worst-case global convergence guarantees and strong empirical performance on large-scale, nonconvex problems.
The Stochastic Frank–Wolfe (SFW) algorithm is proposed, a projection-free framework that leverages linear minimization oracles to bypass expensive projection operations and achieves rigorous convergence rate guarantees for both convex and non-convex objectives.
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