# Case Study: Sparse Signal Reconstruction: a Cardinality Approach

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Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM 1: problem_constr_cardinality
Minimize Meanabs_pen (minimizing L1-error of regression)
subject to
Cardn ≤ Const1 (constraint on cardinality of the solution vector)
Box constraints (bounds on variables)
——————————————————————–
Meanabs_pen = Mean Absolute Penalty
Cardn = Cardinality
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 4096 1024 0 8.07 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data
Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 4096 1024 0.0000999 13.71
PROBLEM 2: problem_minimize_cardinality
Minimize Cardn (minimizing cardinality of the solution vector)
subject to
Meanabs_pen ≤ Const2 (constraint on L1-error of regression)
Box constraints (bounds on variables)
——————————————————————–
Cardn = Cardinality
Meanabs_pen = Mean Absolute Penalty
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 4096 1024 160 900.08 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data
Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 4096 1024 160 900.24
PROBLEM 3: problem_constr_polynomabs
Minimize Meanabs_pen (minimizing L1-error of regression)
subject to
Polynom_abs ≤ Const3 (constraint on the sum of absolute values of the solution vector)
Box constraints (bounds on variables)
——————————————————————–
Meanabs_pen = Mean Absolute Penalty
Polynom_abs = Polynomial Absolute
Box constraints = constraints on individual decision variables
——————————————————————–

Dataset1 4096 1024 0 6.16 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data
Instructions for importing problems from Run-File to PSG MATLAB.

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset2 Problem Statement Data Solution 4096 1024 0.00009836 9.89