# Quadratic Programming (Interior Point) (G Dataflow)

Solves the quadratic programming problem using the interior point method.

## objective function

Coefficients of the quadratic and linear terms of the objective function 0.5x * Q * x + c * x.

### Q

Quadratic term, in the form of a matrix, of the objective function.

### c

Linear term, in the form of a vector, of the objective function.

## start

Values of the variables at which the optimization starts.

## parameter bounds

Upper and lower numeric limits for the parameters being optimized.

### minimum

Smallest allowed values of the parameters being optimized.

This input must be empty or the same size as start. This input must be the same size as maximum. This input does not allow exceptional values, such as Inf, -Inf, or NaN.

### maximum

Greatest allowed values of the parameters being optimized.

This input must be empty or the same size as start. This input must be the same size as minimum. This input does not allow exceptional values, such as Inf, -Inf, or NaN.

## equality constraints

Components of the linear equality constraint equation A * x = b.

### A

Matrix term of the linear equality constraint equation.

### b

Vector term of the linear equality constraint equation.

## inequality constraints

Components of the linear inequality constraint minimumD * xmaximum.

### D

Matrix term of the linear inequality constraint.

### minimum

Smallest allowed value of the linear inequality constraint.

### maximum

Greatest allowed value of the linear inequality constraint.

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## stopping criteria

Conditions that terminate the optimization.

This node terminates the optimization if this node reaches all the tolerance thresholds or passes any of the maximum thresholds.

### function tolerance

Minimum relative change in function values between two internal iterations.

Definition of Relative Change in Function Values

The relative change in function values between two internal iterations is defined as follows:

$\frac{\mathrm{abs}\left({f}_{n}-{f}_{n-1}\right)}{\mathrm{abs}\left({f}_{n}\right)+\epsilon }$

where

• f n is the function value of the current iteration
• f n - 1 is the function value of the previous iteration
• ε is the machine epsilon

Default: 1E-08

### parameter tolerance

Minimum relative change in parameter values between two internal iterations.

Definition of Relative Change in Parameter Values

The relative change in parameter values between two internal iterations is defined as follows:

$\frac{\mathrm{abs}\left({P}_{n}-{P}_{n-1}\right)}{\mathrm{abs}\left({P}_{n}\right)+\epsilon }$

where

• P n is the parameter value of the current iteration
• P n - 1 is the parameter value of the previous iteration
• ε is the machine epsilon

Default: 1E+06

Default: 1E+06

### maximum iterations

Maximum number of iterations that the node runs in the optimization.

Default: 10000

### maximum function calls

Maximum number of calls to the objective function allowed in the optimization.

Default: 10000

### maximum time

Maximum amount of time in seconds allowed for the optimization.

Default: -1 — The optimization never times out.

## minimum

Values of the variables where the objective function has the local minimum.

## f(minimum)

Value of the objective function at minimum.

## Lagrangian multipliers

Coefficients of the Lagrangian function that correspond to the equality and inequality constraints.

If the objective function has three equality constraints and two inequality constraints, the first three Lagrangian multipliers correspond to the equality constraints, and the last two Lagrangian multipliers correspond to the inequality constraints.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application