# Base Optimizer¶

The BaseOptimizer is the underlying object that is used to optimize anything. All other optimizers inherits this class. It offers the most flexibility in modelling.

class allopy.optimize.BaseOptimizer(n, algorithm=40, *args, **kwargs)[source]
__init__(n, algorithm=40, *args, **kwargs)[source]

The BaseOptimizer is the raw optimizer with minimal support. For advanced users, this class will provide the most flexibility. The default algorithm used is Sequential Least Squares Quadratic Programming.

Parameters
• n (int) – number of assets

• algorithm (int or str) – the optimization algorithm

• args – other arguments to setup the optimizer

• kwargs – other keyword arguments

add_equality_constraint(fn, tol=None)[source]

Adds the equality constraint function in standard form, A = b. If the gradient of the constraint function is not specified and the algorithm used is a gradient-based one, the optimizer will attempt to insert a smart numerical gradient for it.

Parameters
• fn (Callable[[ndarray], float]) – Constraint function

• tol (float, optional) – A tolerance in judging feasibility for the purposes of stopping the optimization

Returns

Own instance

Return type

BaseOptimizer

add_equality_matrix_constraint(Aeq, beq, tol=None)[source]

Sets equality constraints in standard matrix form.

For equality, $$\mathbf{A} \cdot \mathbf{x} = \mathbf{b}$$

Parameters
• Aeq – Equality matrix. Must be 2 dimensional

• beq – Equality vector or scalar. If scalar, it will be propagated

• tol – A tolerance in judging feasibility for the purposes of stopping the optimization

Returns

Own instance

Return type

BaseOptimizer

add_inequality_constraint(fn, tol=None)[source]

Adds the equality constraint function in standard form, A <= b. If the gradient of the constraint function is not specified and the algorithm used is a gradient-based one, the optimizer will attempt to insert a smart numerical gradient for it.

Parameters
• fn (Callable[[ndarray], float]) – Constraint function

• tol (float, optional) – A tolerance in judging feasibility for the purposes of stopping the optimization

Returns

Own instance

Return type

BaseOptimizer

add_inequality_matrix_constraint(A, b, tol=None)[source]

Sets inequality constraints in standard matrix form.

For inequality, $$\mathbf{A} \cdot \mathbf{x} \leq \mathbf{b}$$

Parameters
• A – Inequality matrix. Must be 2 dimensional.

• b – Inequality vector or scalar. If scalar, it will be propagated.

• tol – A tolerance in judging feasibility for the purposes of stopping the optimization

Returns

Own instance

Return type

BaseOptimizer

property lower_bounds

Lower bound of each variable

property model

The underlying optimizer. Use this if you need to access lower level settings for the optimizer

optimize(x0=None, *args, initial_solution='random', random_state=None)[source]

Runs the optimizer and returns the optimal results if any.

Notes

An initial vector must be set and the quality of any solution (especially gradient-based ones) will lie on this initial vector. Alternatively, the optimizer will ATTEMPT to randomly generate a feasible one if the initial_solution argument is set to “random”. However, there is no guarantee in the feasibility. In general, it is a tough problem to find a feasible solution in high-dimensional spaces, much more an optimal one. Thus use the random initial solution at your own risk.

The following lists the options for finding an initial solution for the optimization problem. It is best if the user supplies an initial value instead of using the heuristics provided if the user already knows the region to search.

random

Randomly generates “bound-feasible” starting points for the decision variables. Note that these variables may not fulfil the other constraints. For problems where the bounds have been tightly defined, this often yields a good solution.

min_constraint_norm

Solves the optimization problem listed below. The objective is to minimize the $$L_2$$ norm of the constraint functions while keeping the decision variables bounded by the original problem’s bounds.

$\begin{split}\min | constraint |^2 \\ s.t. \\ LB \leq x \leq UB\end{split}$
Parameters
• x0 (iterable float) – Initial vector. Starting position for free variables. In many cases, especially for derivative-based optimizers, it is important for the initial vector to be already feasible.

• args – other arguments to pass into the optimizer

• initial_solution (str, optional) – The method to find the initial solution if the initial vector x0 is not specified. Set as None to disable. However, if disabled, the initial vector must be supplied. See notes on Initial Solution for more information

• random_state (int, optional) – Random seed. Applicable if initial_solution is not None

Returns

Values of free variables at optimality

Return type

ndarray

remove_all_constraints()[source]

Removes all constraints

set_bounds(lb, ub)[source]

Sets the lower and upper bound

Parameters
• lb (Union[ndarray, Iterable, int, float, complex]) – Vector of lower bounds. If array, must be same length as number of free variables. If float or int, value will be propagated to all variables.

• ub (Union[ndarray, Iterable, int, float, complex]) – Vector of upper bounds. If array, must be same length as number of free variables. If float or int, value will be propagated to all variables.

Returns

Own instance

Return type

BaseOptimizer

set_epsilon(eps)[source]

Sets the step difference used when calculating the gradient for derivative based optimization algorithms. This can ignored if you use a derivative free algorithm or if you specify your gradient specifically.

Parameters

eps (float) – The gradient step

Returns

Own instance

Return type

BaseOptimizer

set_epsilon_constraint(eps)[source]

Sets the tolerance for the constraint functions

Parameters

eps (float) – Tolerance

Returns

Own instance

Return type

BaseOptimizer

set_ftol_abs(tol)[source]

Set absolute tolerance on objective function value

Parameters

tol (float) – absolute tolerance of objective function value

Returns

Own instance

Return type

BaseOptimizer

set_ftol_rel(tol)[source]

Set relative tolerance on objective function value

Parameters

tol (float) – Absolute relative of objective function value

Returns

Own instance

Return type

BaseOptimizer

set_lower_bounds(lb)[source]

Sets the lower bounds

Parameters

lb (Union[ndarray, Iterable, int, float, complex]) – Vector of lower bounds. If vector, must be same length as number of free variables. If float or int, value will be propagated to all variables.

Returns

Own instance

Return type

BaseOptimizer

set_max_objective(fn, *args)[source]

Sets the optimizer to maximize the objective function. If gradient of the objective function is not set and the algorithm used to optimize is gradient-based, the optimizer will attempt to insert a smart numerical gradient for it.

Parameters
• fn (Callable) – Objective function

• args – Other arguments to pass to the objective function. This can be ignored in most cases

Returns

Own instance

Return type

BaseOptimizer

set_maxeval(n)[source]

Sets maximum number of objective function evaluations.

After maximum number of evaluations, optimization will stop. Set 0 or negative for no limit.

Parameters

n (int) – maximum number of evaluations

Returns

Own instance

Return type

BaseOptimizer

set_min_objective(fn, *args)[source]

Sets the optimizer to minimize the objective function. If gradient of the objective function is not set and the algorithm used to optimize is gradient-based, the optimizer will attempt to insert a smart numerical gradient for it.

Parameters
• fn (Callable) – Objective function

• args – Other arguments to pass to the objective function. This can be ignored in most cases

Returns

Own instance

Return type

BaseOptimizer

set_stopval(stopval)[source]

Stop when an objective value of at least/most stopval is found depending on min or max objective

Parameters

stopval (float) – Stopping value

Returns

Own instance

Return type

BaseOptimizer

set_upper_bounds(ub)[source]

Sets the upper bound

Parameters

ub (Union[ndarray, Iterable, int, float, complex]) – Vector of lower bounds. If vector, must be same length as number of free variables. If float or int, value will be propagated to all variables.

Returns

Own instance

Return type

BaseOptimizer

set_xtol_abs(tol)[source]

Sets absolute tolerances on optimization parameters.

The tol input must be an array of length n specified in the initialization. Alternatively, pass a single number in order to set the same tolerance for all optimization parameters.

Parameters

tol ({float, ndarray}) – Absolute tolerance for each of the free variables

Returns

Own instance

Return type

BaseOptimizer

set_xtol_rel(tol)[source]

Sets relative tolerances on optimization parameters.

The tol input must be an array of length n specified in the initialization. Alternatively, pass a single number in order to set the same tolerance for all optimization parameters.

Parameters

tol (float or ndarray, optional) – relative tolerance for each of the free variables

Returns

Own instance

Return type

BaseOptimizer

summary()[source]

Prints a summary report of the optimizer

property upper_bounds

Upper bound of each variable