Problem in General (Text) Format of PSG
Contents
The problem described in the previous subsection "Conditional Value-at-Risk minimization" is represented in General (Text) Format of PSG as follows:
minimize cvar_risk(0.95, matrix_scenarios) Constraint: == 1 linear(matrix_budget) Constraint: >= 4.5 avg_g(matrix_scenarios) Box: >=0
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The above problem statement is the reduced version (Short format) of problem statement in Full format (see Problem Statement in General (Text) Format):
Problem: problem_cvar, type = minimize Objective: objective_cvar cvar_risk(0.95, matrix_scenarios) Constraint: constraint_budget, lower_bound = 1, upper_bound = 1 linear(matrix_budget) Constraint: constraint_return, lower_bound = 4.5 avg_g(matrix_scenarios) Box_of_variables: lowerbounds = point_lowerbounds Solver: VAN, precision = 7
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Problem statement includes:
| 1. | Problem name "problem_cvar" and type "minimize". The problem name should coincide with the file name containing the problem description or may be omitted (Brief Description of Optimization Problem). |
| 2. | Objective: |
| • | Objective name "objective_cvar". |
| • | Function name "cvar_risk" in Objective (see PSG Function cvar_risk). |
| • | Matrix name "matrix_scenarios" for "cvar_risk" function. |
| 3. | Constraints: |
| • | Constraint name "constraint_budget" for the first constraint. |
| • | Lower and upper bounds ("lower_bound = 1, upper_bound = 1") for first constraint. |
| • | Function name "linear" in Constraint. |
| • | Matrix name "matrix_budget" in "linear" function . |
| • | Constraint name "constraint_return" for the second constraint. |
| • | Upper bound "lower_bound = 4.5" for second constraint. |
| • | Function name "avg_g" in second constraint (see PSG Function avg_g). |
| • | Matrix name "matrix_scenarios" in "avg_g" function. |
| 4. | Bounds on variables: |
| • | Name of point "point_lowerbounds" containing lower bounds on variables (optional parameter). |
| 5. | Solver parameters: |
| • | Solver "VAN". PSG has four solvers, VAN, CAR, BULDOZER, and TANK. |
| • | Solver precision "precision =7". Solver tries to obtain 7 correct digits in objective and constraints. |
Remarks
| • | The names of matrices and points define the names of text files containing relevant data. |
| • | Data files for this example are in the folder ...\Aorda\PSG\Examples\Problems\Problem_CVaR\ |
| • | The data files with matrices and the file containing the problem description should be in the same folder. |