A unified variance-reduced accelerated gradient method for convex optimization

We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition number, Varag exhibits the unified optimal rates of convergence for solving smooth convex finite-sum problems directly regardless of their strong convexity. Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence. It also establishes an optimal linear rate of convergence for solving a wide class of problems only satisfying a certain error bound condition rather than strong convexity. Varag can also be extended to solve stochastic finite-sum problems.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019

Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph

This paper considers the leader-follower control problem for a linear multi-agent system with directed communication topology and linear nonidentical uncertain coupling subject to integral quadratic constraints (IQCs). A consensus-type control protocol is proposed based on each agent's states relative to its neighbors and leader's state relative to agents which observe the leader. A sufficient condition is obtained by overbounding the cost function. Based on this sufficient condition, a computational algorithm is introduced to minimize the proposed guaranteed bound on tracking performance, which yields a suboptimal bound on the system consensus control and tracking performance. The effectiveness of the proposed method is demonstrated using a simulation example.Comment: Accepted for presentation at the 2013 Australian Control conferenc

N-(2-Chloro-2-nitro-1-phenyl­prop­yl)-4-methyl­benzene­sulfonamide

In the title compound, C16H17ClN2O4S, the dihedral angle between the phenyl and benzene rings is 19.4 (2)°. The crystal packing is stabilized by inter­molecular N—H⋯O hydrogen bonds, as well as by intra- and inter­molecular C—H⋯O hydrogen bonds