Semidefinite Programing (SDP): Difference between revisions
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Minimize <math>C.X \\</math> | Minimize <math>C.X \\</math> | ||
such that <math>A_i X=b_i,i=1,\dots,m \\ X \geq 0</math></p> | such that <math>A_i X=b_i,i=1,\dots,m \\ X \geq 0</math></p> | ||
<p>where <math>C</math> is a symmetric matrix.The objective function is the linear function <math>C.X</math> and there are m linear equations that X must satisfy, namely <math>A_i X = b_i | <p>where <math>C</math> is a symmetric matrix.The objective function is the linear function <math>C.X</math> | ||
,i =1,...,m.</p> | and there are m linear equations that X must satisfy, namely <math>A_i X = b_i,i =1,...,m.</math></p> | ||
Revision as of 13:21, 11 January 2016
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function over the intersection of the cone of positive semidefinite matrices with an affine space.
- Context:
It is an optimization problem of the form:
Minimize [math]\displaystyle{ C.X \\ }[/math]
such that [math]\displaystyle{ A_i X=b_i,i=1,\dots,m \\ X \geq 0 }[/math]
where [math]\displaystyle{ C }[/math] is a symmetric matrix.The objective function is the linear function [math]\displaystyle{ C.X }[/math] and there are m linear equations that X must satisfy, namely [math]\displaystyle{ A_i X = b_i,i =1,...,m. }[/math]