# minimize_lbfgs¶

paddle.incubate.optimizer.functional. minimize_lbfgs ( objective_func, initial_position, history_size=100, max_iters=50, tolerance_grad=1e-08, tolerance_change=1e-08, initial_inverse_hessian_estimate=None, line_search_fn='strong_wolfe', max_line_search_iters=50, initial_step_length=1.0, dtype='float32', name=None ) [source]

Minimizes a differentiable function func using the L-BFGS method. The L-BFGS is simalar as BFGS, the only difference is that L-BFGS use historical sk, yk, rhok rather than H_k-1 to compute Hk. Reference:

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Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006. pp179: Algorithm 7.5 (L-BFGS).

Following summarizes the the main logic of the program based on L-BFGS.Note: _k represents value of k_th iteration, ^T represents the transposition of a vector or matrix. repeat

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compute p_k by two-loop recursion alpha = strong_wolfe(f, x_k, p_k) x_k+1 = x_k + alpha * p_k s_k = x_k+1 - x_k y_k = g_k+1 - g_k rho_k = 1 / (s_k^T * y_k) update sk_vec, yk_vec, rhok_vec check_converge

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end

Parameters
• objective_func – the objective function to minimize. `func` accepts a multivariate input and returns a scalar.

• initial_position (Tensor) – the starting point of the iterates. For methods like Newton and quasi-Newton

• (the initial trial step length should always be 1.0) –

• history_size (Scalar) – the number of stored vector pairs {si,yi}.

• max_iters (Scalar) – the maximum number of minimization iterations.

• tolerance_grad (Scalar) – terminates if the gradient norm is smaller than this. Currently gradient norm uses inf norm.

• tolerance_change (Scalar) – terminates if the change of function value/position/parameter between two iterations is smaller than this value.

• initial_inverse_hessian_estimate (Tensor) – the initial inverse hessian approximation.

• line_search_fn (str) – indicate which line search method to use, only support ‘strong wolfe’ right now. May support ‘Hager Zhang’ in the futrue.

• max_line_search_iters (Scalar) – the maximum number of line search iterations.

• initial_step_length – step length used in first iteration of line search. different initial_step_length

• result. (may cause different optimal) –

• dtype ('float' | 'float32' | 'float64' | 'double') – the data type to be used.

Returns

Indicates whether found the minimum within tolerance. num_func_calls (int): number of objective function called. position (Tensor): the position of the last iteration. If the search converged, this value is the argmin of the objective function regrading to the initial position. objective_value (Tensor): objective function value at the position. objective_gradient (Tensor): objective function gradient at the position.

Return type

is_converge (bool)

Examples

```import paddle

def func(x):