utilities（matlab）—— minFunc

minFunc

minFunc is a Matlab function for unconstrained optimization（无约束最优化） of differentiable real-valued multivariate functions （可微分实值多元函数）using line-search methods（线性搜索）.

接口

function [x,f,exitflag,output] = minFunc(funObj,x0,options,varargin)

% Inputs:
%   funObj - is a function handle
%   x0 - is a starting vector;
%   options - is a struct containing parameters (defaults are used for non-existent or blank fields)
%   varargin{:} - all other arguments are passed as additional arguments to funObj
%
% Outputs:
%   x is the minimum value found
%   f is the function value at the minimum found

（1）既然针对的是可微函数，至少需要为最优化的目标函数提供函数值和一阶梯度的输出，

% f.m
function [y, dy] = f(x)
y = (x-2)^2;
dy = 2*(x-2);

>> minFunc(@f, 0)
Iteration   FunEvals     Step Length    Function Val        Opt Cond
1          2     2.50000e-01     1.00000e+00     2.00000e+00
2          3     1.00000e+00     0.00000e+00     0.00000e+00
Optimality Condition below optTol

ans =

2
% 也即在 x = 2 处取得最小值，

options vs options.Method

options

% Initialize options for minFunc
options.Method = 'cg';
% 'lbfgs'
options.display = 'off';
options.verbose = 0;
options.maxIter = 20;

options.Method

（1）’sd’：Steepest Descent

（2）’cg’: Non-Linear Conjugate Gradient（非线性共轭梯度）