Non User
Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z	Business Non User Industries Finance Tax

Home > Quadratic programming

The quadratic programming problem can be formulated like this:

Assume x belongs to Rⁿ space. The (n x n) matrix E is positive semidefinite and h is any (n x 1) vector.

Minimize (with respect to x)

with at least one instance of the following kind of constraints (if there exists an answer then it satisfies these):

If E is positive definite then f(x) is a convex function and constraints are linear functions. We have from optimization theory that for point x to be an optimum point it is necessary and sufficient that x is a Karush-Kuhn-Tucker (KKT) point.

If there are only equality constraints, then the QP can be solved by a linear system. Otherwise, the most common method of solving a QP is an interior point method, such as LOQO. Active set methods are also commonly used.

External links

• A page about QP
• NEOS guide to QP

Politics	Business	Finance

Topics: Quadratic Programming Point Constraints Optimization Equality...

---

Quadratic equationIn mathematics, a quadratic equation is a polynomial equation of the second degree. The generalized form is : The numbers a b and c are called coefficients a is the coefficient of x''2, b is the coefficient of x and c is the free term or constant. Take, f Quadratic reciprocityIn mathematics, the law of quadratic reciprocity in number theory, conjectured by Euler and Legendre and first satisfactorily proved by Gauss, connects the solvability of two related quadratic equations in modular arithmetic. As a consequence, it allows u Quadratic programmingQuadratic programming (QP) is a special type of mathematical optimization problem. The quadratic programming problem can be formulated like this: Assume x belongs to R n space. The (n x n) matrix E is positive semidefinite and h is any (n x 1) vector. Quadratic functionIn mathematics, a quadratic function is a polynomial function of the form :, where a is nonzero. It takes its name from the Latin quadratus for square, because quadratic functions arise in the calculation of areas of squares. In the case where the domain Quadratic residueIn mathematics, a number q is called a quadratic residue modulo p if there exists an integer x such that: : Otherwise, q is called a quadratic non-residue . In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic w Quadratic formIn mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, the distance between two points in three-dimensional Euclidean space is found by taking the square root of a quadratic form involving six var Quadratic irrational Quadratic field Quadratic integral Quadratic sieve Quadratic residuosity problem