The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem. Many aspects of modern applied research ...

A major advance reveals deep connections between the classes of problems that computers can — and can’t — possibly do. At first glance, the big news coming out of this summer’s conference on the ...

Raz, a professor at Princeton University and the Weizmann Institute of Science, and Tal, a postdoctoral fellow at Stanford University, define a specific kind of computational problem. They prove, with ...

The original version of this story appeared in Quanta Magazine. For computer scientists, solving problems is a bit like mountaineering. First they must choose a problem to solve—akin to identifying a ...

We obtain the optimal order of high-dimensional integration complexity in the quantum computation model in anisotropic Sobolev classes $W_\infty ^r\left( {{{[0,1]}^d ...

A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the ...