Table Of Contents

Linear Programming (Array Input) (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Solves a linear programming problem. This node uses arrays 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.

    connector_pane_image
    datatype_icon

    linear function to maximize

    Vector describing the linear function to maximize.

    datatype_icon

    constraint matrix

    Matrix describing the different constraints.

    datatype_icon

    constraint inequalities

    Vector describing the right sides of the constraints inequalities.

    datatype_icon

    optimization problem

    Optimization problem this node solves.

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

    Default: Maximize

    datatype_icon

    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

    datatype_icon

    optimization cost

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

    datatype_icon

    solution

    Solution vector.

    datatype_icon

    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

    Given that optimization problem is set to Maximize, the following equation defines the optimization problem this node solves.

    cx = max!

    with the constraints x ≥ 0 and Mxb.

    where

    • c is linear function to maximize
    • x is solution
    • M is constraint matrix
    • b is constraint inequalities

    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.

    How to Represent Constraints Using Arrays

    This node uses constraint matrix and constraint inequalties to represent the constraints under which you want to optimize linear function to maximize. You must first organize the constraints in terms of formulas, and then convert the formulas to arrays. The following table explains how to convert the formulas to constraint matrix and constraint inequalties:

    Formulas constraint matrix constraint inequalities
    -0.53 * t1 - 1.07 * t2 - 0.4 * t3 >= -180 -0.53 -1.07 -0.4 -180
    t1 >= 30 1 0 0 30
    t2 >= 30 0 1 0 30
    t3 >= 30 0 0 1 30
    -t1 - t2 - t3 >= -180 -1 -1 -1 -180
    spd-note-note
    Note  

    The formulas can only contain ≥. For example, use -dx ≥ -e instead of dxe, and use the combination of dxe and -dx ≥ -e instead of dx = e.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


    Recently Viewed Topics