Synonyms
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 such...
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Shen, C., van den Hengel, A. (2014). Semidefinite Programming. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_688
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DOI: https://doi.org/10.1007/978-0-387-31439-6_688
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