The performance of each CPU core stopped improving around 2005. The Moore's law, however, continues to apply -- not to single-thread performance -- but the number of cores in each computer. Today, workstations are with 64 cores, graphic cards with thousands of GPU cores, and some cellphones with eight cores are sold at affordable prices. To bene...
Creator:
Yin, Wotao (University of California, Los Angeles)
Created:
2016-01-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider the family of nonnegative homogeneous polynomials of even degree p whose sublevel set G = {x : g(x) ‰¤ 1} (a unit ball) has same fixed volume and want to find in this family the one that minimizes either the parsimony-inducing ell_1-norm or the ell_2-norm of its vector of coefficients. We first show that in both cases this is a conve...
Creator:
Lasserre, Jean Bernard (Centre National de la Recherche Scientifique (CNRS))
Created:
2016-01-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider the problem of the optimal selection of a subset of available sensors or actuators in large-scale dynamical systems. By replacing a combinatorial penalty on the number of sensors or actuators with a convex sparsity-promoting term, we cast this problem as a semidefinite program (SDP). The solution of the resulting convex optimization ...
Creator:
Jovanovic, Mihailo (University of Southern California)
Created:
2017-09-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this series of lectures on continuous optimization, we introduce the area of optimizing over spaces of continuous variables, particularly vectors and matrices of real numbers. The talks will have an algorithmic focus, developing the theory necessary to describe the algorithms and understand their fundamental properties. After describing the l...
Creator:
Wright, Stephen (University of Wisconsin, Madison)
Created:
2016-08-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I will present a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric interpretation, loosely inspired by the ellipsoid method. In 'practice' the new method seems to be superior to Nest...
Creator:
Bubeck, Sébastien (Microsoft)
Created:
2016-01-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. In this talk, we study the problem of completing partially known state statistics. Our aim is to develop tools that can be used in the context of control-oriented modeling of large-scale ...
Creator:
Jovanovic, Mihailo (University of Minnesota, Twin Cities)
Created:
2016-01-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.