modopt.merit_functions

modopt.merit_functions.AugmentedLagrangianIneq(...)

Augmented Lagrangian merit function for pure inequality-constraints of the form c(x) >= 0.

class modopt.merit_functions.AugmentedLagrangianIneq(**kwargs)[source]

Augmented Lagrangian merit function for pure inequality-constraints of the form c(x) >= 0.

Parameters

fcallable: Objective function.
ccallable: Constraint function representing the inequality constraints c(x) >= 0.
gcallable: Objective gradient.
jcallable: Constraint Jacobian.
nxint: Number of optimization/design variables.
ncint: Number of inequality constraints.

Attributes

rhonp.ndarray: Vector of penalty parameters corresponding to each inequality constraint.
cachedict: Dictionary to store the latest function evaluations for ‘f’, ‘c’, ‘g’ and ‘j’. Keys are the function names ‘f’, ‘c’, ‘g’ and ‘j’, and values are tuples of the form (x, f(x)).
eval_countdict: Dictionary to store the number of times each function has been evaluated. Keys are the function names ‘f’, ‘c’, ‘g’ and ‘j’, and values are the number of evaluations.

Methods

`clear_cache`()	Clear the cache of function evaluations.
`compute_function`(v)	Compute the value of the augmented Lagrangian function at the point v.
`compute_gradient`(v)	Compute the gradient of the augmented Lagrangian function at the point v.
`evaluate_function`(x, lag_mult, s, f, c)	Evaluate the augmented Lagrangian function at the point [x, lag_mult, s], given the objective function value f and constraint function values c at the point x.
`evaluate_gradient`(x, lag_mult, s, f, c, g, j)	Evaluate the gradient of the augmented Lagrangian function at the point [x, lag_mult, s], given the objective function f, constraint function c, objective gradient g, and constraint Jacobian j at the point x.
`set_rho`(rho)	Set the penalty parameters rho for the inequality constraints.
`setup`()	Set up the merit function by initializing rho as a vector of zeros.
`update_functions_in_cache`(fnames, x)	Update the function values in the cache for the specified functions in fnames with their values at the given point x.

clear_cache(): Clear the cache of function evaluations.

compute_function(v)[source]

Compute the value of the augmented Lagrangian function at the point v.

Parameters

vnp.ndarray: Point at which to evaluate the augmented Lagrangian function. The point v is a concatenation of the design variables x, Lagrange multipliers lag_mult and slack variables slacks. The point v has the form [x, lag_mult, slacks].

Returns

float: Value of the augmented Lagrangian function at the point v.

compute_gradient(v)[source]

Compute the gradient of the augmented Lagrangian function at the point v.

Parameters

vnp.ndarray: Point at which to evaluate the gradient of the augmented Lagrangian function. The point v is a concatenation of the design variables x, Lagrange multipliers lag_mult and slack variables slacks. The point v has the form [x, lag_mult, slacks].

Returns

np.ndarray: Gradient of the augmented Lagrangian function at the point v.

evaluate_function(x, lag_mult, s, f, c)[source]

Evaluate the augmented Lagrangian function at the point [x, lag_mult, s], given the objective function value f and constraint function values c at the point x.

Parameters

xnp.ndarray: Design variables.
lag_multnp.ndarray: Lagrange multipliers.
snp.ndarray: Slack variables.
ffloat: Objective function value at the point x.
cnp.ndarray: Constraint function values at the point x.

Returns

float: Value of the augmented Lagrangian function at the point x.

evaluate_gradient(x, lag_mult, s, f, c, g, j)[source]

Evaluate the gradient of the augmented Lagrangian function at the point [x, lag_mult, s], given the objective function f, constraint function c, objective gradient g, and constraint Jacobian j at the point x.

Parameters

xnp.ndarray: Design variables.
lag_multnp.ndarray: Lagrange multipliers.
snp.ndarray: Slack variables.
ffloat: Objective function value at the point x.
cnp.ndarray: Constraint function values at the point x.
gnp.ndarray: Objective gradient at the point x.
jnp.ndarray: Constraint Jacobian at the point x.

Returns

np.ndarray: Gradient of the augmented Lagrangian function at the point x.

set_rho(rho)[source]

Set the penalty parameters rho for the inequality constraints.

Parameters

rhonp.ndarray: Penalty parameter vector for the inequality constraints. Must be a 1D numpy array of length nc.

setup()[source]: Set up the merit function by initializing rho as a vector of zeros.

update_functions_in_cache(fnames, x)

Update the function values in the cache for the specified functions in fnames with their values at the given point x. If the cache contains no values for a function in fnames or the cached values correspond to a point other than x, the function is evaluated at x and the cache is updated accordingly.

Parameters

fnamesstr or list of str: Function names whose values need to be updated in the cache. fnames must be one or a subset of [‘f’, ‘g’, ‘c’, ‘j’].
xnp.ndarray: Point at which to update the functions in fnames.