.. _method-surrogate_based_local-merit_function-lagrangian_merit:

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lagrangian_merit
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Use first-order Lagrangian merit function


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**Specification**

- *Alias:* None

- *Arguments:* None


**Description**


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 :cite:p:`Con00`.