fmincon 非线性优化

linprog 线性优化

哦,非常感谢斑竹!不过还想请教一下,线形规划和非线形规划都是指在指定的条件下,函数的最大或者最小值,是这样吗??

[此贴子已经被作者于2008-9-27 10:09:08编辑过]

%LINPROG Linear programming.
%   X=LINPROG(f,A,b) attempts to solve the linear programming problem:
%        
%            min f'*x    subject to:   A*x <= b
%             x
%
%   X=LINPROG(f,A,b,Aeq,beq) solves the problem above while additionally
%   satisfying the equality constraints Aeq*x = beq.
%   
%   X=LINPROG(f,A,b,Aeq,beq,LB,UB) defines a set of lower and upper
%   bounds on the design variables, X, so that the solution is in
%   the range LB <= X <= UB.  Use empty matrices for LB and UB
%   if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below;
%   set UB(i) = Inf if X(i) is unbounded above.

%FMINCON finds a constrained minimum of a function of several variables.
%   FMINCON attempts to solve problems of the form:
%       min F(X)  subject to:  A*X  <= B, Aeq*X  = Beq (linear constraints)
%        X                       C(X) <= 0, Ceq(X) = 0   (nonlinear constraints)
%                                LB <= X <= UB            
%                                                           
%   X=FMINCON(FUN,X0,A,B) starts at X0 and finds a minimum X to the function
%   FUN, subject to the linear inequalities A*X <= B. FUN accepts input X and
%   returns a scalar function value F evaluated at X. X0 may be a scalar,
%   vector, or matrix.
%
%   X=FMINCON(FUN,X0,A,B,Aeq,Beq) minimizes FUN subject to the linear equalities
%   Aeq*X = Beq as well as A*X <= B. (Set A=[] and B=[] if no inequalities exist.)

要注意 fmin系列函数计算出来的很可能是局部最优值
lingprog算出来肯定是全局的 二者在算法上差别很大

linprog适用于有约束条件的线性问题的最小值求解：

X=LINPROG(f,A,b)
         
             f'*x    满足：  A*x <= b
fmincon适用范围最广，适用于非线性约束的非线性函数的最小值求解：

非线性函数：F(X)   
满足：
A*X  <= B, Aeq*X  = Beq
   C(X) <= 0, Ceq(X) = 0   
           LB <= X <= UB
X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB)