# fmin_qp (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Owning Class: optimization

Requires: MathScript RT Module

## Syntax

xmin = fmin_qp(q, c, aineq, bineq)

xmin = fmin_qp(q, c, aineq, bineq, aeq, beq)

xmin = fmin_qp(q, c, aineq, bineq, aeq, beq, min, max)

[xmin, fval] = fmin_qp(q, c, aineq, bineq)

[xmin, fval] = fmin_qp(q, c, aineq, bineq, aeq, beq)

[xmin, fval] = fmin_qp(q, c, aineq, bineq, aeq, beq, min, max)

[xmin, fval, lambda] = fmin_qp(q, c, aineq, bineq)

[xmin, fval, lambda] = fmin_qp(q, c, aineq, bineq, aeq, beq)

[xmin, fval, lambda] = fmin_qp(q, c, aineq, bineq, aeq, beq, min, max)

Legacy Name: `quadprog`

## Description

Computes the minimum of a quadratic function defined by the following expression: 0.5*x'*q*x+c'*x. LabVIEW constrains the computation based on the inputs that you specify.

Examples

## Inputs

Name Description
q Specifies a matrix that is part of the quadratic function whose minimum you want to compute. q is a real, double-precision matrix.
c Specifies a vector that is part of the quadratic function whose minimum you want to compute. c is a real, double-precision vector.
aineq Specifies a matrix for the linear inequality constraints according to the following equation: aineq*xmin <= bineq. aineq can be []. aineq is a real, double-precision matrix.
bineq Specifies a vector for the linear inequality constraints according to the following equation: aineq*xmin <= bineq. bineq must be [] when aineq is []. bineq is a real, double-precision vector.
aeq Specifies a matrix for the linear equality constraints according to the following equation: aeq*xmin = beq. aeq can be []. aeq is a real, double-precision matrix.
beq Specifies a vector for the linear equality constraints according to the following equation: aeq*xmin = beq. beq must be [] when aeq is []. beq is a real, double-precision vector.
min Specifies the lower bound for the solution vector according to the following equation: min <= x <= max. min can be []. min is a real, double-precision vector.
max Specifies the upper bound for the solution vector according to the following equation: min <= x <= max. max can be []. max is a real, double-precision vector.

## Outputs

Name Description
xmin Returns the point at which the quadratic function has the minimum value. xmin is a real, double-precision vector.
fval Returns the value of the quadratic function evaluated at xmin. fval is a real, double-precision scalar.
lambda Returns the lambda values for the solution vector. lambda is a real, double-precision vector.

## Details

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

## Examples

Q = [1, 1; 1, 2];
C = [-2; -6];
AINEQ = [0.5, 0.5; -1, 2];
BINEQ = [1, 2];
MIN = [0; 0];
XMIN = fmin_qp(Q, C, AINEQ, BINEQ, [], [], MIN);