desc.optimize.Optimizer.optimize

Optimizer.optimize(things, objective, constraints=(), ftol=None, xtol=None, gtol=None, ctol=None, x_scale='auto', verbose=1, maxiter=None, options=None, copy=False)Source

Optimize an objective function.

Parameters:

  • things (Optimizable or tuple/list of Optimizable) – Things to optimize, eg Equilibrium.

  • objective (ObjectiveFunction) – Objective function to optimize.

  • constraints (tuple of Objective, optional) – List of objectives to be used as constraints during optimization.

  • ftol (float or None, optional) – Tolerance for termination by the change of the cost function. The optimization process is stopped when dF < ftol * F, and there was an adequate agreement between a local quadratic model and the true model in the last step. If None, defaults to 1e-2 (or 1e-6 for stochastic).

  • xtol (float or None, optional) – Tolerance for termination by the change of the independent variables. Optimization is stopped when norm(dx) < xtol * (xtol + norm(x)). If None, defaults to 1e-6.

  • gtol (float or None, optional) – Absolute tolerance for termination by the norm of the gradient. Optimizer terminates when norm(g) < gtol, where If None, defaults to 1e-8.

  • ctol (float or None, optional) – Stopping tolerance on infinity norm of the constraint violation. Optimization will stop when ctol and one of the other tolerances are satisfied. If None, defaults to 1e-4.

  • x_scale (array, list[dict | 'ess'], 'ess' or 'auto', optional) – Characteristic scale of each variable. Setting x_scale is equivalent to reformulating the problem in scaled variables xs = x / x_scale. An alternative view is that the size of a trust region along jth dimension is proportional to x_scale[j]. Improved convergence may be achieved by setting x_scale such that a step of a given size along any of the scaled variables has a similar effect on the cost function. Default is 'auto', which iteratively updates the scale using the inverse norms of the columns of the Jacobian or Hessian matrix. If set to 'ess', the scale is set using Exponential Spectral Scaling, this scaling is set with two parameters, ess_alpha and ess_order which are passed through options. ess_alpha is the decay rate of the scaling, and ess_order is the norm order for multi-index modes, which can be 1, 2, or np.inf. If not provided in options, the defaults are: ess_alpha=1.2, ess_order=np.inf' and ess_min_value=1e-7 (minimum allowed scale value). If an array, should be the same size as sum(thing.dim_x for thing in things). If a list, the list should have 1 element for each thing, and each element should either be 'ess' to use exponential spectral scaling for that thing, or a dict with the same keys and dimensions as thing.params_dict to specify scales manually.

  • verbose (integer, optional) –

    • 0 : work silently.

    • 1 : display a termination report.

    • 2 : display progress during iterations

  • maxiter (int, optional) – Maximum number of iterations. Defaults to 100.

  • options (dict, optional) –

    Dictionary of optional keyword arguments to override default solver settings. Options that are universal to all optimizers are:

    • "linear_constraint_options" : Dictionary of keyword arguments to pass to LinearConstraintProjection.

    • "perturb_options" : Dictionary of keyword arguments to pass to ProximalProjection as its perturb_options.

    • "solve_options" : Dictionary of keyword arguments to pass to ProximalProjection as its solve_options.

    • "ess_alpha" : float, optional Decay rate of the scaling. Default is 1.2.

    • "ess_order" : int, optional Order of norm to use for multi-index mode numbers, which can be 1, 2, or np.inf. Default is np.inf.

    • "ess_min_value" : float, optional Minimum allowed scale value. Default is 1e-7.

    See the documentation page [Optimizers Supported](https://desc-docs.readthedocs.io/en/stable/optimizers.html) for more details on the options available to each specific optimizer.

  • copy (bool) – Whether to return the current things or a copy (leaving the original unchanged).

Returns:

  • things (list,) – list of optimized things

  • res (OptimizeResult) – The optimization result represented as a OptimizeResult object. Important attributes are: x the solution array, success a Boolean flag indicating if the optimizer exited successfully and message which describes the cause of the termination. See OptimizeResult for a description of other attributes. Additionally, stores the before and after values of the objectives and constraints in the Objective values key.