Blurb::
Use combined penalty and zeroth-order Lagrangian merit function
Description::
Second, the surrogate constraints in the approximate subproblem can be
selected to be surrogates of the original constraints (\c
original_constraints) or linearized approximations to the surrogate
constraints (\c linearized_constraints), or constraints can be omitted
from the subproblem (\c 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 (\c 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 (\c adaptive_penalty_merit), a Lagrangian merit
function which employs first-order Lagrange multiplier updates (\c
lagrangian_merit), or an augmented Lagrangian merit function which
employs both a penalty parameter and zeroth-order Lagrange multiplier
updates (\c 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 \cite Con00.

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