如何使用fminco​n函数求含有积分的函​数的最小值

clc;

clear;

a=0;

alpha=0.01;

beta=0.01;

Caql=1.33;

Crql=1;

b1=3*Caql*(1+a^2)^0.5;

b2=3*Crql*(1+a^2)^0.5;

fun1=@(t)chi2cdf(x(1)*b1^2/(9*x(3)^2)-t^2,x(1)-1)*(normpdf(t+a*x(1)^0.5)+normpdf(t-a*x(1)^0.5));%PN(Caql)

fun2=@(t)chi2cdf(x(1)*b2^2/(9*x(3)^2)-t^2,x(1)-1)*(normpdf(t+a*x(1)^0.5)+normpdf(t-a*x(1)^0.5));%PN(Crql)

fun3=@(t)chi2cdf(x(2)*b1^2/(9*x(3)^2)-t^2,x(2)-1)*(normpdf(t+a*x(2)^0.5)+normpdf(t-a*x(2)^0.5));%PT(Caql)

fun4=@(t)chi2cdf(x(2)*b2^2/(9*x(3)^2)-t^2,x(2)-1)*(normpdf(t+a*x(2)^0.5)+normpdf(t-a*x(2)^0.5));%PT(Crql)

fun=@(x)1/2*((integral(fun3,0,b1*x(2)^0.5/(3*x(3)))*x(1)+(1-integral(fun1,0,b1*x(1)^0.5/(3*x(3))))*x(2))/(1-integral(fun1,0,b1*x(1)^0.5/(3*x(3)))+integral(fun3,0,b1*x(2)^0.5/(3*x(3)))))+...

1/2*((integral(fun4,0,b2*x(2)^0.5/(3*x(3)))*x(1)+(1-integral(fun2,0,b2*x(1)^0.5/(3*x(3))))*x(2))/(1-integral(fun2,0,b2*x(1)^0.5/(3*x(3)))+integral(fun4,0,b2*x(2)^0.5/(3*x(3)))));

x0=[110,130,1.1];

A=[];%AX<=b(线性不等式约束)，G(X)<=0(非线性不等式约束)

b=[];

Aeq=[];%AeqX=beq(线性等式约束)，Geq(X)=0(非线性等式约束)

beq=[];

vlb=[2,2];%lb<=x<=ub(变量约束)

vub=[];

exitflag=1;

[x,fval,exitflag]=fmincon(fun,x0,A,b,Aeq,beq,vlb,vub,'myfun');

function [g,ceq]=myfun(x)

g=1-alpha-(integral(fun3,0,b1*x(2)^0.5/(3*x(3)))/(1-integral(fun1,0,b1*x(1)^0.5/(3*x(3)))+integral(fun3,0,b1*x(2)^0.5/(3*x(3)))));

ceq=(integral(fun4,0,b2*x(2)^0.5/(3*x(3)))/(1-integral(fun2,0,b2*x(1)^0.5/(3*x(3)))+integral(fun4,0,b2*x(2)^0.5/(3*x(3)))))-beta;

[迎迎 孙]

警告: Length of lower bounds is < length(x); filling in missing lower bounds with -Inf.

> In checkbounds (line 33)

In fmincon (line 318)

In trysampling1 (line 24)

未定义函数或变量 'x'。

出错 trysampling1>@(t)chi2cdf(x(2)*b1^2/(9*x(3)^2)-t^2,x(2)-1)*(normpdf(t+a*x(2)^0.5)+normpdf(t-a*x(2)^0.5))

出错 integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

出错 integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

出错 integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

出错 integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

出错

trysampling1>@(x)1/2*((integral(fun3,0,b1*x(2)^0.5/(3*x(3)))*x(1)+(1-integral(fun1,0,b1*x(1)^0.5/(3*x(3))))*x(2))/(1-integral(fun1,0,b1*x(1)^0.5/(3*x(3)))+integral(fun3,0,b1*x(2)^0.5/(3*x(3)))))+1/2*((integral(fun4,0,b2*x(2)^0.5/(3*x(3)))*x(1)+(1-integral(fun2,0,b2*x(1)^0.5/(3*x(3))))*x(2))/(1-integral(fun2,0,b2*x(1)^0.5/(3*x(3)))+integral(fun4,0,b2*x(2)^0.5/(3*x(3)))))

出错 fmincon (line 546)

initVals.f = feval(funfcn{3},X,varargin{:});

出错 trysampling1 (line 24)

[x,fval,exitflag]=fmincon(fun,x0,A,b,Aeq,beq,vlb,vub,'myfun');