# GSLS

`qiskit.algorithms.optimizers.GSLS(maxiter=10000, max_eval=10000, disp=False, sampling_radius=1e-06, sample_size_factor=1, initial_step_size=0.01, min_step_size=1e-10, step_size_multiplier=0.4, armijo_parameter=0.1, min_gradient_norm=1e-08, max_failed_rejection_sampling=50)`

Bases: `Optimizer`

Gaussian-smoothed Line Search.

An implementation of the line search algorithm described in https://arxiv.org/pdf/1905.01332.pdf (opens in a new tab), using gradient approximation based on Gaussian-smoothed samples on a sphere.

This component has some function that is normally random. If you want to reproduce behavior then you should set the random number generator seed in the algorithm_globals (`qiskit.utils.algorithm_globals.random_seed = seed`

).

**Parameters**

**maxiter**(*int*(opens in a new tab)) – Maximum number of iterations.**max_eval**(*int*(opens in a new tab)) – Maximum number of evaluations.**disp**(*bool*(opens in a new tab)) – Set to True to display convergence messages.**sampling_radius**(*float*(opens in a new tab)) – Sampling radius to determine gradient estimate.**sample_size_factor**(*int*(opens in a new tab)) – The size of the sample set at each iteration is this number multiplied by the dimension of the problem, rounded to the nearest integer.**initial_step_size**(*float*(opens in a new tab)) – Initial step size for the descent algorithm.**min_step_size**(*float*(opens in a new tab)) – Minimum step size for the descent algorithm.**step_size_multiplier**(*float*(opens in a new tab)) – Step size reduction after unsuccessful steps, in the interval (0, 1).**armijo_parameter**(*float*(opens in a new tab)) – Armijo parameter for sufficient decrease criterion, in the interval (0, 1).**min_gradient_norm**(*float*(opens in a new tab)) – If the gradient norm is below this threshold, the algorithm stops.**max_failed_rejection_sampling**(*int*(opens in a new tab)) – Maximum number of attempts to sample points within bounds.

## Attributes

### bounds_support_level

Returns bounds support level

### gradient_support_level

Returns gradient support level

### initial_point_support_level

Returns initial point support level

### is_bounds_ignored

Returns is bounds ignored

### is_bounds_required

Returns is bounds required

### is_bounds_supported

Returns is bounds supported

### is_gradient_ignored

Returns is gradient ignored

### is_gradient_required

Returns is gradient required

### is_gradient_supported

Returns is gradient supported

### is_initial_point_ignored

Returns is initial point ignored

### is_initial_point_required

Returns is initial point required

### is_initial_point_supported

Returns is initial point supported

### setting

Return setting

### settings

## Methods

### get_support_level

`get_support_level()`

Return support level dictionary.

**Returns**

A dictionary containing the support levels for different options.

**Return type**

dict (opens in a new tab)[str (opens in a new tab), int (opens in a new tab)]

### gradient_approximation

`gradient_approximation(n, x, x_value, directions, sample_set_x, sample_set_y)`

Construct gradient approximation from given sample.

**Parameters**

**n**(*int*(opens in a new tab)) – Dimension of the problem.**x**(*ndarray*(opens in a new tab)) – Point around which the sample set was constructed.**x_value**(*float*(opens in a new tab)) – Objective function value at x.**directions**(*ndarray*(opens in a new tab)) – Directions of the sample points wrt the central point x, as a 2D array.**sample_set_x**(*ndarray*(opens in a new tab)) – x-coordinates of the sample set, one point per row, as a 2D array.**sample_set_y**(*ndarray*(opens in a new tab)) – Objective function values of the points in sample_set_x, as a 1D array.

**Returns**

Gradient approximation at x, as a 1D array.

**Return type**

### gradient_num_diff

`static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=None)`

We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.

**Parameters**

**x_center**(*ndarray*) – point around which we compute the gradient**f**(*func*) – the function of which the gradient is to be computed.**epsilon**(*float*(opens in a new tab)) – the epsilon used in the numeric differentiation.**max_evals_grouped**(*int*(opens in a new tab)) – max evals grouped, defaults to 1 (i.e. no batching).

**Returns**

the gradient computed

**Return type**

grad

### ls_optimize

`ls_optimize(n, obj_fun, initial_point, var_lb, var_ub)`

Run the line search optimization.

**Parameters**

**n**(*int*(opens in a new tab)) – Dimension of the problem.**obj_fun**(*Callable*(opens in a new tab)*[[**float*(opens in a new tab)*|**ndarray*(opens in a new tab)*],**float*(opens in a new tab)*]*) – Objective function.**initial_point**(*ndarray*(opens in a new tab)) – Initial point.**var_lb**(*ndarray*(opens in a new tab)) – Vector of lower bounds on the decision variables. Vector elements can be -np.inf if the corresponding variable is unbounded from below.**var_ub**(*ndarray*(opens in a new tab)) – Vector of upper bounds on the decision variables. Vector elements can be np.inf if the corresponding variable is unbounded from below.

**Returns**

Final iterate as a vector, corresponding objective function value, number of evaluations, and norm of the gradient estimate.

**Raises**

**ValueError** (opens in a new tab) – If the number of dimensions mismatches the size of the initial point or the length of the lower or upper bound.

**Return type**

tuple (opens in a new tab)[numpy.ndarray (opens in a new tab), float (opens in a new tab), int (opens in a new tab), float (opens in a new tab)]

### minimize

`minimize(fun, x0, jac=None, bounds=None)`

Minimize the scalar function.

**Parameters**

**fun**(*Callable[[POINT],**float*(opens in a new tab)*]*) – The scalar function to minimize.**x0**(*POINT*) – The initial point for the minimization.**jac**(*Callable[[POINT], POINT] | None*) – The gradient of the scalar function`fun`

.**bounds**(*list*(opens in a new tab)*[**tuple*(opens in a new tab)*[**float*(opens in a new tab)*,**float*(opens in a new tab)*]] | None*) – Bounds for the variables of`fun`

. This argument might be ignored if the optimizer does not support bounds.

**Returns**

The result of the optimization, containing e.g. the result as attribute `x`

.

**Return type**

### print_options

`print_options()`

Print algorithm-specific options.

### sample_points

`sample_points(n, x, num_points)`

Sample `num_points`

points around `x`

on the `n`

-sphere of specified radius.

The radius of the sphere is `self._options['sampling_radius']`

.

**Parameters**

**n**(*int*(opens in a new tab)) – Dimension of the problem.**x**(*ndarray*(opens in a new tab)) – Point around which the sample set is constructed.**num_points**(*int*(opens in a new tab)) – Number of points in the sample set.

**Returns**

A tuple containing the sampling points and the directions.

**Return type**

tuple (opens in a new tab)[numpy.ndarray (opens in a new tab), numpy.ndarray (opens in a new tab)]

### sample_set

`sample_set(n, x, var_lb, var_ub, num_points)`

Construct sample set of given size.

**Parameters**

**n**(*int*(opens in a new tab)) – Dimension of the problem.**x**(*ndarray*(opens in a new tab)) – Point around which the sample set is constructed.**var_lb**(*ndarray*(opens in a new tab)) – Vector of lower bounds on the decision variables. Vector elements can be -np.inf if the corresponding variable is unbounded from below.**var_ub**(*ndarray*(opens in a new tab)) – Vector of lower bounds on the decision variables. Vector elements can be np.inf if the corresponding variable is unbounded from above.**num_points**(*int*(opens in a new tab)) – Number of points in the sample set.

**Returns**

Matrices of (unit-norm) sample directions and sample points, one per row. Both matrices are 2D arrays of floats.

**Raises**

**RuntimeError** (opens in a new tab) – If not enough samples could be generated within the bounds.

**Return type**

tuple (opens in a new tab)[numpy.ndarray (opens in a new tab), numpy.ndarray (opens in a new tab)]

### set_max_evals_grouped

`set_max_evals_grouped(limit)`

Set max evals grouped

### set_options

`set_options(**kwargs)`

Sets or updates values in the options dictionary.

The options dictionary may be used internally by a given optimizer to pass additional optional values for the underlying optimizer/optimization function used. The options dictionary may be initially populated with a set of key/values when the given optimizer is constructed.

**Parameters**

**kwargs** (*dict* (opens in a new tab)) – options, given as name=value.

### wrap_function

`static wrap_function(function, args)`

Wrap the function to implicitly inject the args at the call of the function.

**Parameters**

**function**(*func*) – the target function**args**(*tuple*(opens in a new tab)) – the args to be injected

**Returns**

wrapper

**Return type**

function_wrapper