the maximum number of evaluations 是什么
时间: 2024-04-20 17:22:42 浏览: 96
"maximum number of evaluations" 是一个术语,通常用于描述在某个优化问题中允许的最大评估次数。在优化问题中,我们希望通过评估不同的解决方案来找到最优解。每次评估都会计算目标函数的值,然后根据这个值来决定下一个要评估的解决方案。最大评估次数是限制在解决问题过程中进行评估的总次数。
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针对二元函数满足强Wolfe条件的线搜索算法的MATLAB例程
以下是一个针对二元函数满足强Wolfe条件的线搜索算法的MATLAB例程,实现了Armijo条件、曲率条件以及强曲率条件的检查:
```matlab
function [alpha, num_evals] = strong_wolfe_search(f, g, x, p, alpha_init)
% Set the initial values of alpha and other constants
alpha = alpha_init;
c1 = 1e-4;
c2 = 0.9;
max_evals = 100;
num_evals = 0;
% Evaluate the objective function and its gradient at the starting point
f0 = f(x(1), x(2));
g0 = g(x(1), x(2));
% Initialize variables for the strong Wolfe conditions
alpha_lo = 0;
alpha_hi = Inf;
f_lo = f0;
g_lo = g0;
f_hi = f0;
g_hi = g0;
% Loop until the strong Wolfe conditions are satisfied or the maximum
% number of evaluations is reached
while num_evals < max_evals
% Evaluate the objective function and its gradient at the new point
f1 = f(x(1) + alpha*p(1), x(2) + alpha*p(2));
g1 = g(x(1) + alpha*p(1), x(2) + alpha*p(2));
% Check the Armijo condition
if f1 > f0 + c1*alpha*g0'*p
alpha_hi = alpha;
f_hi = f1;
g_hi = g1;
alpha = 0.5*(alpha_lo + alpha_hi);
else
% Check the curvature condition
if g1'*p < c2*g0'*p
alpha_lo = alpha;
f_lo = f1;
g_lo = g1;
alpha = 2*alpha_lo;
else
% Check the strong curvature condition
if g1'*p > -c2*g0'*p
alpha_hi = alpha;
f_hi = f1;
g_hi = g1;
alpha = 0.5*(alpha_lo + alpha_hi);
else
% If all conditions are satisfied, return the current alpha value
alpha_prev = alpha;
num_evals = num_evals + 1;
return;
end
end
end
% Update the number of function evaluations used
num_evals = num_evals + 1;
% If the maximum number of evaluations is reached, return the current alpha value
if num_evals == max_evals
alpha_prev = alpha;
fprintf('Maximum number of function evaluations reached\n');
return;
end
end
% Return the number of function evaluations used
if num_evals == max_evals
fprintf('Maximum number of function evaluations reached\n');
end
end
```
该例程采用了传统的回溯线搜索算法,并在此基础上添加了强曲率条件的检查。在每次迭代中计算一个新的alpha值,然后检查是否满足Armijo条件、曲率条件和强曲率条件。如果满足所有三个条件,则返回当前的alpha值。如果没有满足,则根据条件更新alpha值并继续迭代,直到达到最大迭代次数或满足条件为止。
请注意,此代码仅为演示目的。在实际应用中,您可能需要根据您的需求进行修改。
满足Wolfe条件的线搜索算法的MATLAB例程
以下是一个简单的MATLAB例程,演示了如何实现满足Wolfe条件的线搜索算法:
```matlab
function [alpha, num_evals] = wolfe_search(f, g, x, p, alpha_init)
% Set the initial values of alpha and other constants
alpha = alpha_init;
c1 = 1e-4;
c2 = 0.9;
max_evals = 100;
num_evals = 0;
% Evaluate the objective function and its gradient at the starting point
f0 = f(x);
g0 = g(x);
% Loop until the Wolfe conditions are satisfied or the maximum number of
% evaluations is reached
while num_evals < max_evals
% Evaluate the objective function and its gradient at the new point
f1 = f(x + alpha*p);
g1 = g(x + alpha*p);
% Check the Armijo condition
if f1 > f0 + c1*alpha*g0'*p
break;
end
% Check the curvature condition
if g1'*p < c2*g0'*p
break;
end
% If both conditions are satisfied, return the current alpha value
alpha_prev = alpha;
alpha = 0.5*(alpha + alpha_init);
num_evals = num_evals + 1;
end
% Return the number of function evaluations used
if num_evals == max_evals
fprintf('Maximum number of function evaluations reached\n');
end
end
```
该例程采用了传统的回溯线搜索算法,在每次迭代中计算一个新的alpha值,然后检查是否满足Armijo条件和曲率条件。如果两个条件都得到满足,就返回当前的alpha值。如果没有满足,则将alpha值减半并继续迭代,直到达到最大迭代次数或满足条件为止。
请注意,此代码仅为演示目的。在实际应用中,您可能需要根据您的需求进行修改。