constrainted regularization to solve ill conditioned problems?
I am trying to solve a matrix equation of the form Ax = b (solving for x with known A and b).
prior to trying regularisation I was using lsqlin (https://uk.mathworks.com/help/optim/ug/lsqlin.html) with the constraints lsqlin(C,d,[],[],[],[],lb,ub) where lb and ub are lower and upper bounds for the allowed values of my output vector. Some (but not all) of my vector values in x should not have negative values. My results are ill-conditioned. I was wondering if anyone is aware of any type of regularisation (e.g. Tikhonov) that has lb or ub constraints such that I can make some (but not all) of my values in x non-negative?
For context:
I have tried using Tikhonov regularisation (the example code given here: https://uk.mathworks.com/matlabcentral/fileexchange/130259-arls-automatically-regularized-least-squares?s_tid=prof_contriblnk – the response from 15 Mar 2024). The issue is that this code does not have any constraints.I am trying to solve a matrix equation of the form Ax = b (solving for x with known A and b).
prior to trying regularisation I was using lsqlin (https://uk.mathworks.com/help/optim/ug/lsqlin.html) with the constraints lsqlin(C,d,[],[],[],[],lb,ub) where lb and ub are lower and upper bounds for the allowed values of my output vector. Some (but not all) of my vector values in x should not have negative values. My results are ill-conditioned. I was wondering if anyone is aware of any type of regularisation (e.g. Tikhonov) that has lb or ub constraints such that I can make some (but not all) of my values in x non-negative?
For context:
I have tried using Tikhonov regularisation (the example code given here: https://uk.mathworks.com/matlabcentral/fileexchange/130259-arls-automatically-regularized-least-squares?s_tid=prof_contriblnk – the response from 15 Mar 2024). The issue is that this code does not have any constraints. I am trying to solve a matrix equation of the form Ax = b (solving for x with known A and b).
prior to trying regularisation I was using lsqlin (https://uk.mathworks.com/help/optim/ug/lsqlin.html) with the constraints lsqlin(C,d,[],[],[],[],lb,ub) where lb and ub are lower and upper bounds for the allowed values of my output vector. Some (but not all) of my vector values in x should not have negative values. My results are ill-conditioned. I was wondering if anyone is aware of any type of regularisation (e.g. Tikhonov) that has lb or ub constraints such that I can make some (but not all) of my values in x non-negative?
For context:
I have tried using Tikhonov regularisation (the example code given here: https://uk.mathworks.com/matlabcentral/fileexchange/130259-arls-automatically-regularized-least-squares?s_tid=prof_contriblnk – the response from 15 Mar 2024). The issue is that this code does not have any constraints. tikhonov, regularisation, ill-conditioned, ill conditioned, matrix equation, constraints, constrained equations MATLAB Answers — New Questions