Many numerical optimization problems of interest today are large dimensional, and techniques to solve them efficiently are thus an active field of research. A very powerful class of algorithms for the solution of large problems is that of multi-level methods. Originally, the concept of a method exploiting multiple levels, i.e., multiple resolutions of an underlying problem, was introduced for the solution of large scale systems arising from the discretization of partial differential equations (PDEs). In this context these methods are known as multigrid (MG) methods for the linear case or full approximation schemes (FAS) for the nonlinear one [3, 38]. These schemes were later extended to nonlinear optimization problems, in which context they are known as multi-level optimization techniques [27, 11, 12, 13, 5]. The central idea of all these approaches is to use the structure of the problem in order to significantly reduce the computational cost compared to standard approaches applied to the full unstructured problem. In this paper we introduce a new interpretation of multi-level methods as block coordinate descent (BCD) methods: iterations at coarse levels (i.e., low resolution) can be interpreted as the (possibly approximate) solution of a subproblem involving a set of variables smaller than that required to describe the fine level (high resolution). We propose a framework that allows us to encompass multi-level methods for several classes of problems as well as a unifying complexity analysis based on a generic block coordinate descent, which is simple yet comprehensive.

An analytics revolution comes for every sport sooner or later. MLB had Moneyball in the early 2000s and has moved well beyond it in the years since. The NBA has used efficiency to all but kill the mid-range jump shot. Soccer has seen an influx of countless new ways to measure passes and scoring chances down to the finest detail. The NFL's change became most evident in 2018. Computer models that looked at thousands of games found an inefficiency: Coaches were being too conservative on fourth down, when teams can either punt the ball away or go for an all-or-nothing conversion.

The hovercraft concept is not a new one, having floated drivers across land, sand and water since the 1950s. But 70 years on, now petrol heads finally have a reason to celebrate the vehicle, because what has been billed as the world's first ever luxury sports hovercraft is set to go on sale for $100,000 (£73,400). It may not be as quick as a supercar, with a top speed of around 60mph and 120 miles of range at 40 mph, but it's the fastest amphibious vehicle yet. And unlike a Ferrari, McLaren or Bugatti, this exciting new roadster travels on a cushion of air seven inches off the ground, allowing drivers to whizz across water and giving new meaning to the term off-road vehicle. Designed by the firm Von Mercier, which is named after British engineer and founder Michael Mercier, the Arosa is said to'blend cutting-edge hovercraft and electric vehicle innovation'.

Machine learning is an integral part of Pittsburgh's tech economy, thanks to Carnegie Mellon University's position as one of the nation's foremost research centers on the topic. That's enticed tech giants such as Google and Uber to set up shot in the Steel City. Pittsburghers have varied knowledge on what machine learning is. On a crisp afternoon on Carnegie Mellon University's campus, Adeline Mercier of Squirrel Hill was walking with her young daughter on campus. She said her husband works in machine learning.

The North Atlantic Treaty Organization (NATO) believes in incorporating artificial intelligence (A.I.) in its decision-making process, a senior official told CNBC. The 68-year-old military alliance must be prepared for the prospect of A.I. delivering strategic verdicts on key NATO issues, said General Denis Mercier, Supreme Allied Commander Transformation of NATO. "The key issue is the distribution of data -- how we can, through that, empower subordinate levels of command, when it's necessary, to take action," he said on the sidelines of the Shangri-La Dialogue in Singapore. Such a vision is "the next step," Mercier continued. "That's not what we do today but this is really what we need to be available to do in the future."

Notman House is a local ICT mecca in Montreal. Google's $3.4 million investment in the Montreal Institute for Learning Algorithms (MILA) and new lab opening in The City of Saints not only highlights the company's banking on artificial intelligence, but its faith in Canada's ICT industries to help it in that quest. Montreal is running neck and neck with Toronto and Vancouver to attract talent and incubate businesses. Though Ontario holds a lead over it, Montreal remains, "the second most popular location for most types of ICT jobs" after Toronto according to the Canadian Information and Communications Technology Council, and over 222,000 people are employed across various industries, from gaming to AI R&D. The lab will be led by University of Montreal and Twitter alumnus Hugo Larochelle, whose like-minded associates at MILA are already heavily invested in deep learning applications.