Optimization Seminar - Subgradient methods for huge-scale optimization problems

Event Details
  • Date/Time:
    • Tuesday April 3, 2012
      5:30 pm - 6:30 pm
  • Location: ISyE Executive Classroom
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Contact

Dr. Renato Monteiro  renato.monteiro@isye.gatech.edu

Summaries

Summary Sentence: Subgradient methods for huge-scale optimization problems

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TITLE: Subgradient methods for huge-scale optimization problems

SPEAKER: Yuri Nesterov

ABSTRACT:

We consider a new class of huge-scale problems, the problems with sparse subgradients. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity of corresponding linear operators, we suggest a very efficient implementation of subgradient iterations, which total cost depends logarithmically in the dimension. This technique is based on a recursive update of the results of matrix/vector products and the values of symmetric functions. It works well, for example, for matrices with few nonzero diagonals and for max-type functions.

We show that the updating technique can be efficiently coupled with the simplest subgradient methods, the unconstrained minimization method by B. Polyak, and the constrained minimization scheme by N. Shor. Similar results can be obtained for a new non- smooth random variant of a coordinate descent scheme. We present also the promising results of preliminary computational experiments.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Anita Race
  • Workflow Status: Published
  • Created On: Mar 26, 2012 - 7:01am
  • Last Updated: Oct 7, 2016 - 9:58pm