Vector Optimization Problem - What should I use?

Which function should I use for the problem below?

I have a given matrix of order . I need to find the vector of order that minimizes ; subject to

1 - , where is a given vector of order

2 -

3 - , where l and u are given scalar constraints.

Thanks for any help.

[Torsten]

https://de.mathworks.com/help/gads/ga.html

[Süleyman Polat]

@Torsten Thanks for answering. Can you look at this code?

P = [-45 -30 -30 -20 -35 -30 -40 -20 -25;
    -45 -40 -25 -20 -20 -15 -15 -20 -30;
    -45 -40 -30 -25 -25 -30 -30 -25 -30];
b = [-100; -100; -100];
fun = @(x) (norm(P*x));
lb = [0; 0; 0; 0; 0; 0; 0; 0; 0];
ub = [1; 1; 1; 1; 1; 1; 1; 1; 1];
intcon = 1:9;
x = ga(fun, 9, P, b, [], [], lb, ub, [], intcon);

It gives the error

"Undefined function 'ga' for input arguments of type 'function_handle'."

I'm assuming it has something to do with "fun", but I'm not very knowledgable in MATLAB.

Edit: I have MATLAB 2016b, and I have ga.m in my toolbox.

Edit 2: And this code

x = ga(@(norm(P*x)),9,P,b,[],[],lb,ub,[],intcon);

gives the error

"Unbalanced or unexpected parenthesis or bracket."

[Torsten]

What is the result of using the

ver

command?

Run it from a script or in your Command Window.

If you have a license to use "ga", then look in ga.m on how to call it. Maybe it has changed since 2016.

[Süleyman Polat]

@Torsten ver command shows me my MATLAB version and such. It has Global Optimization Toolbox as well. Here's my ga.m function.

function [x,fval,exitFlag,output,population,scores] = ga(fun,nvars,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,intcon,options)

Maybe the problem is nonlcon variable. I put an empty matrix there. Since I used intcon, I was supposed to put empty matrices for Aeq and beq, and I did that as well.

When I use the

which -all ga

command it shows

C:\Program Files\MATLAB\R2016b\toolbox\globaloptim\globaloptim\ga.m % Has no license available

Does that mean have a license for MATLAB, but don't have for ga.m?

[Walter Roberson]

It means you do not have a license for the Global Optimization Toolbox

[Matt J]

@Süleyman Polat You aren't allowed to post ga.m or other copyrighted Matlab material in the forum.

[Süleyman Polat]

@Walter Roberson Thanks, seems like it. Is there a way for me to solve this then (apart from buying the toolbox)?

[Torsten]

The "ver" command shows you the licenced toolboxes.

If the global optimization toolbox is listed, you should be able to use "ga".

The input vector to FITNESSFCN is a row vector ; so maybe you'll have to use

fun = @(x) norm(P*x.')

[Süleyman Polat]

@Torsten ver command DOES list Global Optimization Toolbox Version 3.4.1

Changing to

fun = @(x) (norm(P*x.'))

still gives the error

"Undefined function 'ga' for input arguments of type 'function_handle'.".

[Walter Roberson]

@Torsten

ver() shows the installed toolboxes, not the licensed toolboxes.

C:\Program Files\MATLAB\R2016b\toolbox\globaloptim\globaloptim\ga.m % Has no license available

is specific: you do not have the license for the globaloptimation toolbox.

You can find various genetic algorithm implementations in the File Exchange.

[Torsten]

Thank you - good to know.

There is no command to list the licensed toolboxes ?

[Walter Roberson]

temp = arrayfun(@(M){char(M.getName), license('test',char(M.getFlexName))}, com.mathworks.product.util.ProductIdentifier.values, 'UniformOutput', false);
temp = vertcat(temp{:});
licensed_products = temp([temp{:,2}]==1,1)

licensed_products = 112×1 cell array
    {'5G Toolbox'                        }
    {'Aerospace Toolbox'                 }
    {'Aerospace Blockset'                }
    {'Antenna Toolbox'                   }
    {'Audio Toolbox'                     }
    {'Powertrain Blockset'               }
    {'AUTOSAR Blockset'                  }
    {'Bioinformatics Toolbox'            }
    {'Communications Toolbox'            }
    {'MATLAB Compiler'                   }
    {'MATLAB Compiler SDK'               }
    {'Control System Toolbox'            }
    {'Curve Fitting Toolbox'             }
    {'Data Acquisition Toolbox'          }
    {'Database Toolbox'                  }
    {'Datafeed Toolbox'                  }
    {'DDS Blockset'                      }
    {'Deep Learning HDL Toolbox'         }
    {'DO Qualification Kit'              }
    {'Automated Driving Toolbox'         }
    {'DSP System Toolbox'                }
    {'Embedded Coder'                    }
    {'Econometrics Toolbox'              }
    {'HDL Verifier'                      }
    {'Spreadsheet Link'                  }
    {'Financial Toolbox'                 }
    {'Financial Instruments Toolbox'     }
    {'Fixed-Point Designer'              }
    {'Sensor Fusion and Tracking Toolbox'}
    {'Fuzzy Logic Toolbox'               }