This lesson shows how to create and solve optimization problem using PSG m-functions. All MATLAB operations are in the file: ./Aorda/PSG/MATLAB/Examples/Toolbox/Example_CVaR_Toolbox.m

 

 

Step 1. Pack data to PSG format

 

Define input data in MATLAB Command Window:

 

H=[1,4,8,3; 7,5,4,6; 2,8,1,0; 0,3,4,9];

c=[0.2; 0.11; 0.6; 0.1];

Aeq=[1, 1, 1, 1];

lb=[0; 0; 0; 0];

vars={'x1', 'x2', 'x3', 'x4'};

 

Pack input data to PSG structure containing headers and data (see Main Objects of PSG MATLAB):

 

Create PSG matrix 'matrix_scenarios' (see tbpsg_matrix_pack):

 

toolboxstruc_arr(1) = tbpsg_matrix_pack('matrix_scenarios',H,vars,c);

 

Create PSG matrix 'matrix_budget' (see tbpsg_matrix_pack):

 

toolboxstruc_arr(2) = tbpsg_matrix_pack('matrix_budget',Aeq,vars);

 

Create PSG point 'point_lowerbounds' (see tbpsg_point_pack):

 

toolboxstruc_arr(3) = tbpsg_point_pack('point_lowerbounds',lb,vars);

 

Step 2. Prepare Problem Statement in General (text) Format

 

Problem statement syntax is described in Problem Statement in MATLAB.

Create the following variable in MATLAB:

 

problem_statement = sprintf('%s\n',...

'minimize',...

'  cvar_risk(0.95, matrix_scenarios)',...

'Constraint: >= 4.5',...

'  avg_g(matrix_scenarios)',...

'Constraint: == 1',...

'  linear(matrix_budget)',...

'Box: >= point_lowerbounds');

 

Step 3. Solve optimization problem

 

Solve optimization problem programmatically (see tbpsg_run):

 

>> [solution_str,outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);

 

All results will be saved to the text report "solution_str" and structure "outargstruc_arr" (see PSG Solution in MATLAB).

 

Step 4. Extract solution details

 

Convert PSG Solution to structure using tbpsg_solution_struct:

 

output_structure = tbpsg_solution_struct(solution_str, outargstruc_arr);

 

>> output_structure

 

output_structure =

 

             status: {'optimal'}

          objective: -4.350000000000000

    constraint_name: {2x1 cell}

   constraint_value: [2x1 double]

      function_name: {3x1 cell}

     function_value: [3x1 double]

               time: [0 0.180000000000000 0]

         point_data: [0 0.599999999999997 0.190000000000002 0.210000000000001]

         point_vars: {'x1'  'x2'  'x3'  'x4'}

        matrix_data: {}

        matrix_vars: {}

        vector_data: {}

 

Save values of function to the new variable using:

 

>> output = tbpsg_function_data(solution_str, outargstruc_arr)

 

output =

 

   4.5000

  -4.3500

   1.0000

 

Full list of available PSG m-functions for extracting solution details: Extract Solution Results Functions.

 

Step 5. Edit problem in Toolbox

 

Open current problem in Toolbox Window (see tbpsg_toolbox):

 

>> tbpsg_toolbox(problem_statement, toolboxstruc_arr);

 

 

The following screen will be opened:

 

 

You can edit this problem using Toolbox Window (change problem statement and input data). For example, delete the second constraint:

 

 

Press button "Solve" to start solving the optimization problem.