Semidefinite Programing (SDP): Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
Line 3: | Line 3: | ||
** <p>It is an optimization problem of the form: | ** <p>It is an optimization problem of the form: | ||
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> | ||
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 A_i X = b_i | |||
,i =1,...,m.</p> |
Revision as of 13:17, 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 A_i X = b_i
,i =1,...,m.