Computer Vision

2014 Edition
| Editors: Katsushi Ikeuchi

Semidefinite Programming

  • Chunhua Shen
  • Anton van den Hengel
Reference work entry



Semidefinite programming is a subtopic of convex optimization. Convex optimization refers to minimization of a convex function subject to a set of convex constraints. Semidefinite programming involves minimization of a linear objective function over the intersection of linear constraints and the cone of positive semidefinite matrices. Clearly, semidefinite programming is a special case of convex optimization.


Many computer vision problems can be formulated as convex optimization problems. The main advantage of convex optimization is that if a local minimum exists, then it is also a global minimum. In other words, the convexity guarantees to attain the global optimum if it exists.

In a semidefinite programming problem, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Semidefinite programming unifies a few standard problems...

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Chunhua Shen
    • 1
  • Anton van den Hengel
    • 1
  1. 1.School of Computer Science, The University of AdelaideAdelaide, SAAustralia