Problem Formulation
The quadratic programming problem can be formulated as:
Assume x belongs to space. Both x and c are column vectors with n elements (n×1 matrices), and Q is a symmetric n×n matrix.
Minimize (with respect to x)
Subject to one or more constraints of the form:
- (inequality constraint)
- (equality constraint)
where indicates the vector transpose of . The notation means that every entry of the vector is less than or equal to the corresponding entry of the vector .
If the matrix is positive semidefinite, then is a convex function: In this case the quadratic program has a global minimizer if there exists some feasible vector (satisfying the constraints) and if is bounded below on the feasible region. If the matrix is positive definite and the problem has a feasible solution, then the global minimizer is unique.
If is zero, then the problem becomes a linear program.
A related programming problem, quadratically constrained quadratic programming, can be posed by adding quadratic constraints on the variables.
Read more about this topic: Quadratic Programming
Famous quotes containing the words problem and/or formulation:
“If we parents accept that problems are an essential part of life’s challenges, rather than reacting to every problem as if something has gone wrong with universe that’s supposed to be perfect, we can demonstrate serenity and confidence in problem solving for our kids....By telling them that we know they have a problem and we know they can solve it, we can pass on a realistic attitude as well as empower our children with self-confidence and a sense of their own worth.”
—Barbara Coloroso (20th century)
“Art is an experience, not the formulation of a problem.”
—Lindsay Anderson (b. 1923)