功能
找到最小的无约束多变量函数
min f(x)
x
where f(x) is a function that returns a scalar(标量).
x is a vector or a matrix;
语法
x = fminunc(fun,x0)
x = fminunc(fun,x0,options)
x = fminunc(problem)
[x,fval] = fminunc(___)
[x,fval,exitflag,output] = fminunc(___)
[x,fval,exitflag,output,grad,hessian] = fminunc(___)
描述
x = fminunc(fun,x0)从x0开始,尝试寻找fun中描述的函数的局部最小值x。 点x0可以是标量,矢量或矩阵
x = fminunc(fun,x0,options)使选项中指定的优化选项最小化。 使用optimoptions来设置这些选项。
x = fminunc(problem) finds the minimum for problem, where problem is a structure described in Input Arguments. Create the problem structure by exporting a problem from Optimization app, as described in Exporting Your Work.
[x,fval] = fminunc(___),对于任何语法,返回的解x
[x,fval,exitflag,output] = fminunc(___)另外返回一个描述fminunc退出条件的值exitflag,以及一个带有关于优化过程信息的结构输出。
[x,fval,exitflag,output,grad,hessian] = fminunc(___)另外返回:
grad — Gradient of fun at the solution x
hessian — Hessian of fun at the solution x. See fminunc Hessian.
例子
Step 1: Write a file objfun.m.
function f = objfun(x)
f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);
Step 2: Set options.
设置选项以使用“quasi-newton”算法。 设置选项是因为“trust-region”算法要求目标函数包含渐变。 如果您没有设置选项,那么根据您的MATLAB®版本,fminunc可以发出警告。
options = optimoptions(@fminunc,'Algorithm','quasi-newton');
Step 3: Invoke fminunc using the options.
x0 = [-1,1]; % Starting guess
[x,fval,exitflag,output] = fminunc(@objfun,x0,options);
结果
Local minimum found.
Optimization completed because the size of the gradient is less than
the default value of the optimality tolerance.
<stopping criteria details>
x =
0.5000 -1.0000
fval =
3.6609e-15
exitflag =
1
output =
iterations: 8
funcCount: 66
stepsize: 6.3361e-07
lssteplength: 1
firstorderopt: 1.2284e-07
algorithm: 'quasi-newton'
message: 'Local minimum found.…'