applyPenaltyLpIteration(datasets,LHS,RHS,c):

Start with a small penalty parameter and solve the Lp-regularized optimization problem, increase the penalty parameter until physical requirements are fulfilled.

Input Arguments

  • datasets

  • LHS - left hand side of symmetric linear system

  • RHS - right hand side of symmetric linear system

  • c - see config

Output Arguments

  • theta - material parameters

applyPenaltyLpRandomStart(datasets,LHS,RHS,c):

Solve the Lp-regularized optimization problem with random initial guesses.

Input Arguments

  • datasets

  • LHS - left hand side of symmetric linear system

  • RHS - right hand side of symmetric linear system

  • c - see config

Output Arguments

  • theta - material parameters

  • at_least_one_converged - information about the convergence

applyPenaltyLpThreshold(datasets,LHS,RHS,theta,c):

Solve the Lp-regularized optimization problem for a given initial guess using fixed-point iteration. During the iterative process, the threshold algorithm is applied.

Input Arguments

  • datasets

  • LHS - left hand side of symmetric linear system

  • RHS - right hand side of symmetric linear system

  • theta - initial guess of material parameters

  • c - see config

Output Arguments

  • theta - material parameters

  • converged - information about the convergence

checkLocalMinimumLp(datasets,theta,c):

Check if the provided solution is a local minimum of the cost function.

Input Arguments

  • datasets

  • theta - material parameters

  • c - see config

Output Arguments

  • none

computeCostLp(datasets,theta,c):

Compute cost function for L2 minimization with Lp-regularization.

Input Arguments

  • datasets

  • theta - material parameters

  • c - see config

Output Arguments

  • Cost_weak - cost corresponding to the weak linear momentum balance

  • Cost_penaltyLp - cost corresponding to the Lp-regularization

  • Cost_total - total cost

saveResultsLp(theta,c,counter_load=None):

Save the results and the chosen parameters in a text file.

Input Arguments

  • theta - material parameters

  • c - see config

  • counter_load - current load step

Output Arguments

  • none