Matlab fmincon函数

文章目录

函数功能

获取约束的非线性多变量函数的最小值
样式：

其中,c(x), ceq(x) 分别表示非线性的约束条件，而A, Aeq表示的是线性约束。

函数表达及用法

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

1. fun
   minimizes fun
2. 初始值
   starts at x0，x0 can be a scalar, vector, or matrix.
3. 线性约束
   attempts to find a minimizer x of the function described in fun subject to the linear inequalities Ax ≤ b，Aeqx = beq，and the range lb ≤ x ≤ ub
4. 非线性约束
   the nonlinear inequalities c(x) or equalities ceq(x) defined in nonlcon
   For example,

   x = fmincon(@myfun,x0,A,b,Aeq,beq,lb,ub,@mycon)
   where mycon is a MATLAB function such as
   function [c,ceq] = mycon(x)
   c = ...     % Compute nonlinear inequalities at x.
   ceq = ...   % Compute nonlinear equalities at x.
   

5. 选项
   Optimization options, specified as the output of optimoptions or a structure such as optimset returns
   
   
6. Algorithm
   

返回值

[x,fval,exitflag,output,lambda,grad,hessian] = fmincon(___) additionally returns:

x— variable
fval— the value of the objective function fun
exitflag— describes the exit condition of fmincon,
output— a structure output with information about the optimization process.
lambda — Structure with fields containing the Lagrange multipliers at the solution x.
grad — Gradient of fun at the solution x.
hessian — Hessian of fun at the solution x. See fmincon Hessian.

1. exitflag
   
2. output
   
3. lambda
   
4. Hessian