Use combined penalty and zeroth-order Lagrangian merit function


  • Alias: None

  • Arguments: None


Second, the surrogate constraints in the approximate subproblem can be selected to be surrogates of the original constraints ( original_constraints) or linearized approximations to the surrogate constraints ( linearized_constraints), or constraints can be omitted from the subproblem ( no_constraints). Following optimization of the approximate subproblem, the candidate iterate is evaluated using a merit function, which can be selected to be a simple penalty function with penalty ramped by SBL iteration number ( penalty_merit), an adaptive penalty function where the penalty ramping may be accelerated in order to avoid rejecting good iterates which decrease the constraint violation ( adaptive_penalty_merit), a Lagrangian merit function which employs first-order Lagrange multiplier updates ( lagrangian_merit), or an augmented Lagrangian merit function which employs both a penalty parameter and zeroth-order Lagrange multiplier updates ( augmented_lagrangian_merit). When an augmented Lagrangian is selected for either the subproblem objective or the merit function (or both), updating of penalties and multipliers follows the approach described in [CGT00].