Numerical algebraic geometry and semidefinite programming

Dataset

Description

Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations. By considering this in the context of numerical algebraic geometry, we employ numerical algebraic geometric techniques such as adaptive precision path tracking, endgames, and projective space to accurately solve semidefinite programs. We develop feasibility tests for both primal and dual problems which can distinguish between the four feasibility types of semidefinite programs. Finally, we couple our feasibility tests with facial reduction to develop a solving approach that can handle every scenario, including problems with nonzero duality gap. Various examples are used to demonstrate the new methods with comparisons to commonly used semidefinite programming software.

Attributes

Attribute NameValues
Creator
  • Jonathan Hauenstein

  • Alan Liddell

  • Sanesha McPherson

  • Yi Zhang

Publisher
  • Jonathan Hauenstein

Departments and Units
Record Visibility Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0D798G4

This DOI is the best way to cite this dataset.

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