Computer Vision

2014 Edition
| Editors: Katsushi Ikeuchi

Semidefinite Programming

• Chunhua Shen
• Anton van den Hengel
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-31439-6_688

Definition

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.

Background

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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