SELECTION_AUTOMATIC - selects from all choices of lambda_p a solution vector with both low cost and low lp-(semi)-norm

Comments

Given multiple solutions of material parameters and their corresponding costs and lp-(semi)-norm values, this function selects the solution which has both a low cost and a low lp-(semi)-norm. The selection procedure depends on a hyperparameter (threshold_factor_cost), which influences how sparse the solution should be, and a hyperparameter (threshold_factor_parameters), determining below which value parameters should be discarded.

Input Arguments

lambda_p (double) - regularization factors

parameters (double) - multiple solutions of material parameters (every row corresponds to one solution)

norm_lp (double) - lp-(semi)-norm values (without considering weighting factor lambda_p)

cost_without_regularizer (double) - cost function values of the given solutions minus the regularization terms (considering weighting factor lambda_p)

threshold_factor_cost (double) - factor for computing the cost threshold C^{th}

min_cost_threshold (double) - minimum value of the cost threshold C^{th}

Output Arguments

lambda_p_select (double) - selected regularization factor

parameters_select (double) - selected solution of the material parameters

norm_lp_select (double) - selected lp-(semi)-norm value

cost_without_regularizer_select (double) - selected cost function value