# Linear Programming (Formula Input) (G Dataflow)

Solves a linear programming problem. This node uses formulas to represent the linear function to optimize and the constraints.

To solve the optimization problem, an optimal vector must exist. This node returns an error if an optimal vector does not exist.  ## objective function

Linear function to maximize or minimize. The formula can contain any number of valid variables.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores. ## subject to constraints

Constraints under which you want to optimize the objective function. The formula can contain any number of valid variables. Note

You must enter inequalities in subject to constraints. The inequalities can only contain ≥. For example, enter -dx ≥ -e instead of dxe, and enter the combination of dxe and -dx ≥ -e instead of dx = e.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores. ## optimization problem

Optimization problem this node solves.

Name Description
Maximize Solves a maximization problem.
Minimize Solves a minimization problem.

Default: Maximize ## 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 ## optimization cost

Maximum or minimum value, if it exists, of the solution vector under the constraints. ## solution

Solution vector. The nth element in solution returns the optimal solution of the nth element in objective function. ## 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.

## How this Node Solves an Optimization Problem

The solution to a linear programming problem is a two-step process. This node completes the following steps to solve a linear programming problem.

1. Transforms the original problem into a problem in restricted normal form, essentially without inequalities in the formulation.
2. Solves the restricted normal form problem.

To find the minimum value of f(x, y) = x + y under the constraint x ≥ 0 and y ≥ 2, enter the following values on the panel:

 objective function x + y subject to constraints (x >= 0, y >= 2)

This node returns 2 as optimization cost and (0, 2) as solution, where the nth element in solution is the optimal solution of the nth variable in objective function.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices