I am trying to solve a least squares problem where the objective function has a least squares term along with L1 and L2 norm regularization. I am unable to find which matlab function provides the ability to perform such an optimization in addition to specifying constraints. I looked into the MATLAB optimization toolbox which also does not provide too much freedom to specify own objective functions (although I hope I am wrong in this case!) in the case of leastSquares optimization problems. If anyone knows how to model such an optimization problem in matlab please do help me out. The optimization problem is as follows:
Here aj is an m X 1 vector and A is an mXn matrix , wj is an n x 1 vector. I don't know how to incorporate the two additional regularization terms into the optimization problems as they only accept 2 matrices and perform the least squares operation on them. I would like to know how to implement this objective function and pass it into matlab optimization toolbox leastSquares function. Any help would be appreciated. If not in the optimization toolbox, alternative implementations of this problem in CPLEX using matlab would also be helpful.
thanks in advance!