Presented By: U-M Industrial & Operations Engineering
Departmental Seminar (899): Jon Lee, University of Michigan
Sparse Generalized Inverses
The Departmental Seminar Series is open to all. U-M Industrial and Operations Engineering graduate students and faculty are especially encouraged to attend.
The seminar will be followed by a reception in the IOE Commons (Room 1709) from 4 p.m. to 5 p.m.
Title:
Sparse Generalized Inverses
Abstract:
Generalized inverses are ubiquitous in matrix algebra and its applications, in particular in statistics. The most commonly-used generalized inverse is the well-known and celebrated Moore-Penrose pseudo-inverse. But not all Moore-Penrose properties are needed to ensure that a generalized inverse solves key problems, like least squares. So there is the opportunity to find sparser generalized inverses that do the jobs. The usual approach of exact 1-norm minimization to induce sparsity has flaws here, so we will look at an alternative approach overcoming the flaws. I will present theoretical and computational results on this, in particular approximation algorithms with nice properties. Based on joint works with: Marcia Fampa (Universidade Federal do Rio de Janeiro), Luze Xu (UM), and Gabriel Ponte (Universidade Federal do Rio de Janeiro).
Bio:
Jon’s research focus is on nonlinear discrete optimization (NDO). Many practical engineering problems have physical aspects which are naturally modeled through smooth nonlinear functions, as well as design aspects which are often modeled with discrete variables. Research in NDO seeks to marry diverse techniques from classical areas of optimization, for example methods for smooth nonlinear optimization and methods for integer linear programming, with the idea of successfully attacking natural NDO models for practical engineering problems.
The seminar will be followed by a reception in the IOE Commons (Room 1709) from 4 p.m. to 5 p.m.
Title:
Sparse Generalized Inverses
Abstract:
Generalized inverses are ubiquitous in matrix algebra and its applications, in particular in statistics. The most commonly-used generalized inverse is the well-known and celebrated Moore-Penrose pseudo-inverse. But not all Moore-Penrose properties are needed to ensure that a generalized inverse solves key problems, like least squares. So there is the opportunity to find sparser generalized inverses that do the jobs. The usual approach of exact 1-norm minimization to induce sparsity has flaws here, so we will look at an alternative approach overcoming the flaws. I will present theoretical and computational results on this, in particular approximation algorithms with nice properties. Based on joint works with: Marcia Fampa (Universidade Federal do Rio de Janeiro), Luze Xu (UM), and Gabriel Ponte (Universidade Federal do Rio de Janeiro).
Bio:
Jon’s research focus is on nonlinear discrete optimization (NDO). Many practical engineering problems have physical aspects which are naturally modeled through smooth nonlinear functions, as well as design aspects which are often modeled with discrete variables. Research in NDO seeks to marry diverse techniques from classical areas of optimization, for example methods for smooth nonlinear optimization and methods for integer linear programming, with the idea of successfully attacking natural NDO models for practical engineering problems.
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