Invited Session Tue.3.H 1012

Tuesday, 15:15 - 16:45 h, Room: H 1012

Cluster 17: Nonsmooth optimization [...]

Large-scale structured optimization


Chair: Anatoli Juditsky



Tuesday, 15:15 - 15:40 h, Room: H 1012, Talk 1

Arkadi Nemirovski
Randomized first-order algorithms for bilinear saddle point problems and their applications to l1 minimization

Coauthors: Anatoli Juditsky, Fatma Kilinc-Karzan


In this talk, we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number of applications, primarily to the problems of l1 minimization arising in sparsity-oriented Signal Processing.
We demonstrate, both theoretically and by numerical examples, that when seeking for medium-accuracy
solutions of large-scale l1 minimization problems, our randomized algorithms outperform
significantly (and progressively as the sizes of the problems grow) the state-of-the-art
deterministic methods.



Tuesday, 16:15 - 16:40 h, Room: H 1012, Talk 3

Sergey Shpirko
Primal-dual subgradient method for huge-scale conic optimization problems and its applications in structural design

Coauthor: Yurii Nesterov


For huge-scale optimization problems, we suggest a new primal-dual
subgradient method. It generates the main minimization sequence in the
dual space. At the same time, it constructs an approximate primal
solution. Our scheme is based on the recursive updating technique
suggested recently by Nesterov. It allows a logarithmic dependence of the
total cost of subgradent iteration in the number of variables.
As an application, we consider a classical problem of finding an
optimal design of mechanical structures. Such a problem can be posed
in a conic form, with high sparsity of corresponding linear operator.


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