TEST PROBLEMS
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Case study background and problem formulations
PROBLEM: L1 Relaxed
Minimize Meanabs_pen (minimizing L1-error of regression)
subject to
Polynom_abs ≤ Const2 (constraint on the sum of absolute values of the components of decision vector)
Box constraints (bounds on variables)
——————————————————————–
Meanabs_pen = Mean Absolute Penalty
Polynom_abs = Polynomial Absolute
Box constraints = constraints on individual decision variables
——————————————————————–
Problem “problem_601_Relaxed”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 3200 | 6.48E+00 | 55.33 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data | ||
R | R Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 3200 | 2.78E+00 | 1965.0 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 3200 | 8.42E-01 | 2894.0 |
Dataset4 | ProblemStatement | Data | Solution | 4096 | 3200 | 9.18E-08 | 509.2 |
Problem “problem_602_Relaxed”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 3200 | 6.80E+00 | 190.26 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data | ||
R | R Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 3200 | 2.99E+00 | 2906.6 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 3200 | 3.60E-01 | 2982.0 |
Dataset4 | ProblemStatement | Data | Solution | 4096 | 3200 | 9.71E-05 | 272.6 |
Minimize Meanabs_pen (minimizing L1-error of regression)
subject to
Linear ≤ Const1 (constraint on sum of components of decision vector)
Box constraints (bounds on variables)
——————————————————————–
Meanabs_pen = Mean Absolute Penalty
Box constraints = constraints on individual decision variables
——————————————————————–Problem “problem_2_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 1.22E+00 | 0.5 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 6.63E-01 | 0.6 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.42E-02 | 4.5 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.24E-014 | 2.8 |
Problem “problem_3_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 1024 | 6.38E-01 | 0.5 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 1024 | 8.03E-02 | 4.1 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 1024 | 2.27E-03 | 130.3 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 1024 | 4.58E-14 | 460.3 |
Problem “problem_5_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 300 | 1.00E+00 | 0.5 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 300 | 2.71E-01 | 8.0 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 300 | 5.79E-02 | 1.8 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 300 | 2.43E-14 | 1.8 |
Problem “problem_6_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 600 | 1.41E+02 | 1.4 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 600 | 6.62E+01 | 56.5 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 600 | 1.59E+00 | 185.9 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 600 | 3.77E-12 | 30.9 |
Problem “problem_7_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2560 | 600 | 5.81E-02 | 2.3 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2560 | 600 | 3.39E-02 | 7.9 |
Dataset3 | ProblemStatement | Data | Solution | 2560 | 600 | 1.02E-02 | 12.8 |
Dataset4 | ProblemStatemen | Data | Solution | 2560 | 600 | 1.37E-13 | 1.6 |
Problem “problem_8_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2560 | 600 | 4.94E-02 | 6.0 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2560 | 600 | 1.64E-02 | 11.9 |
Dataset3 | ProblemStatement | Data | Solution | 2560 | 600 | 3.29E-03 | 11.6 |
Dataset4 | ProblemStatement | Data | Solution | 2560 | 600 | 1.36E-13 | 1.2 |
Problem “problem_9_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 128 | 128 | 3.14E-01 | 0.01 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 128 | 128 | 9.30E-02 | 0.02 |
Dataset3 | ProblemStatement | Data | Solution | 128 | 128 | 7.81E-03 | 0.02 |
Dataset4 | ProblemStatement | Data | Solution | 128 | 128 | 2.92E-13 | 0.04 |
Problem “problem_10_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 1.32E-01 | 0.5 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 6.10E-02 | 0.6 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.15E-02 | 0.7 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.64E-12 | 143.1 |
Problem “problem_11_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 256 | 1.22E+00 | 3.1 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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|
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 256 | 5.18E-01 | 6.5 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 256 | 1.29E-01 | 35.5 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 256 | 2.53E-14 | 31.6 |
Problem “problem_603_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 1024 | 3.35E-01 | 2.2 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 1024 | 1.75E-01 | 10.7 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 1024 | 4.16E-02 | 1150.4 |
Dataset4 | ProblemStatement | Data | Solution | 4096 | 1024 | 2.32E-14 | 391.0 |
Problem “problem_902_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1000 | 200 | 2.32E-02 | 0.07 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1000 | 200 | 1.86E-02 | 0.12 |
Dataset3 | ProblemStatement | Data | Solution | 1000 | 200 | 3.60E-03 | 0.12 |
Dataset4 | ProblemStatement | Data | Solution | 1000 | 200 | 3.12E-14 | 26.3 |
Problem “problem_903_Relaxed_Double”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 6.17E-01 | 0.6 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data |
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) |
Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.06E-01 | 1.4 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 9.92E-02 | 29.7 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 9.18E-05 | 10.7 |
Minimize Meansquare + Linear (minimizing L2-error of regression)
subject to
Linear ≤ Const3 (constraint on sum of components of decision vector)
Box constraints (bounds on variables)
——————————————————————–
Meansquare = Mean Square Penalty
Meanabs_pen = Mean Absolute Penalty
Box constraints = constraints on individual decision variables
——————————————————————–Problem “problem_2_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 2.98E+03 | 0.32 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 2.31E+03 | 0.32 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.15E+02 | 0.32 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.47E+01 | 0.32 |
Dataset5 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.50E+00 | 0.31 |
Problem “problem_3_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 1024 | 2.37E+03 | 1.4 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 1024 | 1.31E+03 | 1.4 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 1024 | 1.78E+02 | 2.7 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 1024 | 2.16E+01 | 10.8 |
Dataset5 | ProblemStatement | Data | Solution | 2048 | 1024 | 2.22E+00 | 102.8 |
Problem “problem_5_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 300 | 2.10E+03 | 1.6 |
---|---|---|---|---|
Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 300 | 1.23E+03 | 1.9 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 300 | 1.58E+02 | 8.8 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 300 | 1.78E+01 | 85.7 |
Dataset5 | ProblemStatement | Data | Solution | 2048 | 300 | 1.82E+00 | 837.4 |
Problem “problem_6_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2048 | 600 | 1.29E+07 | 1.8 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2048 | 600 | 5.29E+06 | 2.4 |
Dataset3 | ProblemStatement | Data | Solution | 2048 | 600 | 1.46E+06 | 9.5 |
Dataset4 | ProblemStatement | Data | Solution | 2048 | 600 | 1.70E+05 | 87.4 |
Dataset5 | ProblemStatement | Data | Solution | 2048 | 600 | 1.76E+04 | 636.5 |
Dataset6 | ProblemStatement | Data | Solution | 2048 | 600 | 4.20E+03 | 112.4 |
Dataset7 | ProblemStatement | Data | Solution | 2048 | 600 | 4.60E+02 | 6.4 |
Problem “problem_7_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2560 | 600 | 2.25E+00 | 2.03 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2560 | 600 | 1.56E+00 | 3.00 |
Dataset3 | ProblemStatement | Data | Solution | 2560 | 600 | 8.90E-01 | 2.52 |
Dataset4 | ProblemStatement | Data | Solution | 2560 | 600 | 1.96E-01 | 2.88 |
Problem “problem_8_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 2560 | 600 | 2.11E+00 | 2.76 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 2560 | 600 | 1.52E+00 | 3.00 |
Dataset3 | ProblemStatement | Data | Solution | 2560 | 600 | 8.81E-01 | 3.24 |
Dataset4 | ProblemStatement | Data | Solution | 2560 | 600 | 1.95E-01 | 5.91 |
Problem “problem_9_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 128 | 128 | 1.68E+02 | 0.48 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 128 | 128 | 1.16E+02 | 0.98 |
Dataset3 | ProblemStatement | Data | Solution | 128 | 128 | 3.65E+01 | 1.47 |
Dataset4 | ProblemStatement | Data | Solution | 128 | 128 | 5.54E+00 | 2.41 |
Dataset5 | ProblemStatement | Data | Solution | 128 | 128 | 3.98E+00 | 2.40 |
Problem “problem_10_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 2.04E+03 | 150.9 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 6.66E+02 | 281.3 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.15E+02 | 441.9 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.01E+02 | 651.7 |
Dataset5 | ProblemStatement | Data | Solution | 1024 | 1024 | 2.07E+01 | 1848.6 |
Problem “problem_11_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 256 | 1.80E+03 | 0.5 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1024 | 256 | 2.33E+02 | 1.9 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 256 | 2.40E+01 | 20.0 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 256 | 2.40E+00 | 179.4 |
Dataset5 | ProblemStatement | Data | Solution | 1024 | 256 | 7.19E-01 | 1.1 |
Problem “problem_601_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 3200 | 8.78E+05 | 204.8 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 3200 | 2.46E+05 | 800.8 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 3200 | 1.91E+05 | 1215.5 |
Dataset4 | ProblemStatement | Data | Solution | 4096 | 3200 | 5.61E+05 | 2179.5 |
Dataset5 | ProblemStatement | Data | Solution | 4096 | 3200 | 1.05E+06 | 473.6 |
Problem “problem_602_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 3200 | 3.62E+05 | 687.5 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 3200 | 2.66E+05 | 679.8 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 3200 | 2.94E+05 | 255.5 |
Problem “problem_603_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 4096 | 1024 | 1.21E+02 | 6.6 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 4096 | 1024 | 2.14E+01 | 18.6 |
Dataset3 | ProblemStatement | Data | Solution | 4096 | 1024 | 2.54E+00 | 168.3 |
Problem “problem_902_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1000 | 200 | 1.01E-01 | 0.3 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
Dataset2 | ProblemStatement | Data | Solution | 1000 | 200 | 1.67E-02 | 0.5 |
Dataset3 | ProblemStatement | Data | Solution | 1000 | 200 | 1.73E-03 | 2.0 |
Problem “problem_903_L2_dbl”
# of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | |
Dataset1 | 1024 | 1024 | 8.70E+02 | 68.1 |
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Environments | ||||
Run-File | Problem Statement | Data | Solution | |
Matlab Toolbox | Data | |||
Matlab Subroutines | Matlab Code | Data |
Download other datasets in Run-File Environment.
Instructions for importing problems from Run-File to PSG MATLAB.
Sources of Data | |||||||
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Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
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Dataset2 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.18E+02 | 167.2 |
Dataset3 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.29E+01 | 170.9 |
Dataset4 | ProblemStatement | Data | Solution | 1024 | 1024 | 1.41E+00 | 263.0 |
Dataset5 | ProblemStatement | Data | Solution | 1024 | 1024 | 4.58E-01 | 530.4 |
SPARCO is a suite of problems for testing and benchmarking algorithms for sparse signal reconstruction, Berg et al. (2007, 2008). It is also an environment for creating new test problems. Also a suite of standard linear operators is provided from which new problems can be assembled. SPARCO is implemented entirely in MATLABand is self contained.
This case study presents problem formulations and its solutions for a set of sparse reconstruction problems taken from SPARCO toolbox.
Problems included in the SPARCO toolbox were initially considered by different authors in different application areas: imaging, compressed sensing, geophysics, information compressing, etc. Relevant references can be found in the SPARCO toolbox.
The objective of Sparse Reconstruction is to find a decision vector which has a small number of non-zero components and satisfies exactly or almost exactly a system of linear equations. There are many variants of optimization formulations of such problems.
This case study is described in paper Boyko et al. (2011).
We solved many problems included in SPARCO toolbox problems in so called “L1Relaxed D” formulation. “L1Relaxed D” minimizes L1-error of regression with one linear inequality on the sum of decision vector components; the decision vector components are nonnegative (number of decision variables is doubled to achieve non-negativity). The non-negativity of variables is quite important because an optimal vector contains many zero variables. To investigate property of solution we solved various problems with different values of upper bound in the linear inequality and calculated cardinality and max functions in optimal points.
Some problems were solved in so called “L1Relaxed” formulation with original set of variables (without doubling the number of variables to achieve non-negativity). Variables are bounded by box constraints in this formulation. For these problems “L1Relaxed” formulation is more effective compared to “L1Relaxed D” formulation.
Additionally many problems were solved in so called “L2 D” or LASSO formulation which also has double set of variables but does not have constraints.
Sum of decision variables multiplied by some coefficient is used as regularization term in the objective function.
This problem can be easy solved by methods for unconstrained optimization.
We used SPARCO toolbox software to extract data for the considered problems. SPARCO toolbox provides a set of operators to deal with data.
We converted the problems data to PSG format and solved them in PSG Run-File environment.
objective: objective_new, linearize = 1
meanabs_pen_obj(matrix_ab602)
constraint: constraint_card, upper_bound = 700, linearize = 1
polynom_abs_S(matrix_card4096)
0 * cardn_1(1.,matrix_card4096)
0 * cardn_2(0.1,matrix_card4096)
0 * cardn_3(0.01,matrix_card4096)
0 * cardn_4(0.001,matrix_card4096)
0 * cardn_5(0.0001,matrix_card4096)
0 * cardn_6(0.00001,matrix_card4096)
0 * max_comp_pos_7(matrix_card4096)
0 * max_comp_neg_8(matrix_card4096)
box_of_variables: lowerbounds = -40, upperbounds = +40
Solver: van, precision = 4, stages = 6, timelimit = 3600
Timing: Data_loading_time = 11.97, Preprocessing_time = 0.69, Solving_time = 272.61
Variables: optimal_point = point_problem_602_Relaxed_700
Objective: objective_new = 9.71029929057e-005
Constraint: constraint_card = 6.968284830013e+002 [-3.171516998665e+000] Function: meanabs_pen_obj(matrix_ab602) = 9.710299290575e-005
Function: polynom_abs_s(matrix_card4096) = 6.968284830013e+002
Function: cardn_1(0.100000E+01,matrix_card4096) = 1.420000000000e+002
Function: cardn_2(0.100000E+00,matrix_card4096) = 7.890000000000e+002
Function: cardn_3(0.100000E-01,matrix_card4096) = 3.043000000000e+003
Function: cardn_4(0.100000E-02,matrix_card4096) = 3.964000000000e+003
Function: cardn_5(0.100000E-03,matrix_card4096) = 4.079000000000e+003
Function: cardn_6(0.100000E-04,matrix_card4096) = 4.095000000000e+003
Function: max_comp_pos_7(matrix_card4096) = 1.616083034336e+001
Function: max_comp_neg_8(matrix_card4096) = 6.562008879305e+000
• Berg, E.V., Friedlander, M.P., Hennenfent, G., Herrmann, F., Saab, R., and O., Yilmaz (2007): SPARCO: A testing framework for sparse reconstruction. Tech. Rep. TR-2007-20, Dept. Computer Science, University of British Columbia, Vancouver.
• Berg, E.V., and M.P., Friedlander (2008): SPARCO: A toolbox for testing sparse reconstruction algorithms. URL http://www.cs.ubc.ca/labs/scl/sparco/
• Boyko, N., Karamemis, G., Kuzmenko, V. and S. Uryasev (2011): Sparse Signal Reconstruction: a Cardinality Approach. Submitted for publication (Download the paper).