Flexible identity: Difference between revisions
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In [[linear programming]], a discipline within [[applied mathematics]], a '''basic''' solution''' is any solution of a linear programming problem satisfying certain specified technical conditions. | |||
For a [[polyhedron]] <math>P</math> and a vector <math> \mathbf{x}^* \in \mathcal{R}^n</math>, <math>\mathbf{x}^*</math> is a '''basic solution''' if: | |||
# All the equality constraints defining <math>P</math> are active at <math>\mathbf{x}^*</math> | |||
# Of all the constraints that are active at that vector, at least <math>n</math> of them must be [[linear independence| linearly independent]]. Note that this also means that at least <math>n</math> constraints must be active at that vector.<ref>{{cite book|last1=Bertsimas|first1=Dimitris|last2=Tsitsiklis|first2=John N.|title=Introduction to linear optimization|year=1997|publisher=Athena Scientific|location=Belmont, Mass.|isbn=978-1-886529-19-9|pages=50|url=http://athenasc.com/linoptbook.html}}</ref> | |||
A constraint is ''active'' for a particular solution <math>\mathbf{x}</math> if it is satisfied at equality for that solution. | |||
A basic solution that satisfies all the constraints defining <math>P</math> or in other words, one that lies within <math>P</math> is called a '''basic feasible solution'''. | |||
==References== | |||
<references /> | |||
[[Category:Linear programming]] | |||
Latest revision as of 06:31, 23 May 2013
Template:Underlinked Template:Orphan
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions.
For a polyhedron and a vector , is a basic solution if:
- All the equality constraints defining are active at
- Of all the constraints that are active at that vector, at least of them must be linearly independent. Note that this also means that at least constraints must be active at that vector.[1]
A constraint is active for a particular solution if it is satisfied at equality for that solution.
A basic solution that satisfies all the constraints defining or in other words, one that lies within is called a basic feasible solution.
References
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