有约束最优化问题 matlab,请教一个Matlab关于有约束最优化问题

朴灿烈づ我的快乐病毒、 2023-01-13 10:52 117阅读 0赞

先谢谢大家了，就是我因为初学，编的都很简单，希望大家不要笑我啊

function newfinger

clc;clear;

x0=\[30,30,0,0,25,0,5,5,0,0,0,0,0,0,10,50,10,10,30,10,5,5,5\];

lb=\[30,30,0,0,25,0,5,5,0,0,0,0,0,0,10,50,10,10,30,10,5,5,5\];

ub=\[126,92,101,101,125,101,30,30,pi/2,pi/2,pi/2,pi/2,pi/2,pi/2,80,70,40,40,70,40,30,30,100\];

options = optimset('Algorithm','active-set');

\[x,f\]=fmincon(@fingerobjfunc,x0,\[\],\[\],\[\],\[\],lb,ub,@fingernlconstr,options)

smallestmoment=f

function\[C,Ceq\]=fingernlconstr(x)

s0=x(1);y0=x(2);s1=x(3);y1=x(4);s2=x(5);y2=x(6);f1=x(7);f2=x(8);c1=x(9);c2=x(10);c3=(11);c4=x(12);c5=x(13);c6=x(14);s3=x(15);y3=x(16);s4=x(17);y4=x(18);s5=x(19);y5=x(20);f3=x(21);f4=x(22);f5=x(23);

C(1)=30-abs(y0-s0\*atan(c1))/sqrt(1+atan(c1)^2);                                         %C(1)-C(6)为几何条件的约束，表示球心到关节板直线的距离大于30；

C(2)=30-abs(y0-atan(c1+c2)\*(s0-46\*sin(c1))-46\*cos(c1))/sqrt(1+atan(c1+c2)^2);

C(3)=30-abs(y0-atan(c1+c2+c3)\*(s0-46\*sin(c1)-34\*sin(c1+c2))-46\*cos(c1)-34\*cos(c1+c2))/sqrt(1+atan(c1+c2+c3)^2);

C(4)=30-abs(y0-s0\*tan(c4)+25\*tan(c4))/sqrt(1+tan(c4)^2);

C(5)=30-abs(y0-tan(c4+c5)\*(s0-25-46\*cos(c4))-46\*sin(c4))/sqrt(1+tan(c4+c5)^2);

C(6)=30-abs(y0-tan(c4+c5+c6)\*(s0-46\*cos(c4)-34\*cos(c4+c5)-25)-46\*sin(c4)-34\*sin(c4+c5))/sqrt(1+tan(c4+c5+c6)^2);

C(7)=(s1-46\*sin(c1)-34.5\*sin(c1+c2))^2+(y1-46\*cos(c1)-34.5\*cos(c1+c2))^2-21^2;      %C(7)-C(11)表示接触点在指节长度范围内

C(8)=(s2-25-46\*cos(c4)-34\*cos(c4+c5))^2+(y2-46\*sin(c4)-34\*sin(c4+c5))^2-21^2;

C(9)=(s3-25-46\*cos(c4)-34\*cos(c4+c5))^2+(y3-46\*sin(c4)-34\*sin(c4+c5))^2-28^2;

C(10)=(s4-46\*sin(c1))^2+(y4-46\*cos(c1))^2-40^2;

C(11)=(s5-25)^2+(y4)^2-40^2;

C(12)=30-0.3\*(f1+f2+f3+f4+f5);

C(13)=s1-s0;   %保证接触点在圆柱的各半平面内

C(14)=s0-s2;

C(15)=s3-s0;

C(16)=s4-s0;

C(17)=s0-s5;

Ceq(1)=y1-atan(c1+c2+c3)\*(s1-46\*sin(c1)-34\*sin(c1+c2))-46\*cos(c1)-34\*cos(c1+c2);    %几何条件的线性等式约束，表示接触点在指节板所在直线及园曲线方程上

Ceq(2)=(s1-s0)^2+(y1-y0)^2-900;

Ceq(3)=y2-tan(c4+c5+c6)\*(s2-25-46\*cos(c4)-34\*cos(c4+c5))-46\*sin(c4)-34\*sin(c4+c5);

Ceq(4)=(s2-s0)^2+(y2-y0)^2-900;

Ceq(5)=f1\*sin(c1+c2+c3)+f3\*sin(c1+c2)+f4\*sin(c1)-f2\*sin(c4+c5+c6)-f5\*sin(c4);       %%修改力平衡方程式

Ceq(6)=f1\*cos(c1+c2+c3)+f3\*cos(c1+c2)-f4\*cos(c1)+f2\*cos(c4+c5+c6)+f5\*cos(c4);       %%修改力平衡方程式

Ceq(7)=y3-atan(c1+c2)\*(s3-46\*sin(c1))-46\*cos(c1);                      %接触点在指节及圆柱的平面曲线上

Ceq(8)=(s3-s0)^2+(y3-y0)^2-900;

Ceq(9)=y4-atan(c1)\*s4;

Ceq(10)=(s4-s0)^2+(y4-y0)^2-900;

Ceq(11)=y5-atan(c4)\*(s5-25);

Ceq(12)=(s5-s0)^2+(y5-y0)^2-900;

function f=fingerobjfunc(x)

s0=x(1);y0=x(2);s1=x(3);y1=x(4);s2=x(5);y2=x(6);f1=x(7);f2=x(8);c1=x(9);c2=x(10);c3=(11);c4=x(12);c5=x(13);c6=x(14);s3=x(15);y3=x(16);s4=x(17);y4=x(18);s5=x(19);y5=x(20);f3=x(21);f4=x(22);f5=x(23);

f=4\*900/(900-(f1\*(46\*cos(c2+c3)+34\*cos(c3)+sqrt((s1-46\*sin(c1)-34\*sin(c1+c2))^2+(y1-46\*cos(c1)-34.5\*cos(c1+c2))^2))+f4\*sqrt((s4-46\*sin(c1))^2+(y4-46\*cos(c1))^2)+f3\*(46\*cos(c2)+sqrt((s3-46\*sin(c1))^2+(y3-46\*cos(c1))^2)))^2)+...

4\*900/(900-(f1\*(34.5\*cos(c3)+sqrt((s1-46\*sin(c1)-34\*sin(c1+c2))^2+(y1-46\*cos(c1)-34.5\*cos(c1+c2))^2))+f3\*sqrt((s3-46\*sin(c1))^2+(y3-46\*cos(c1))^2))^2)+...

4\*900/(900-(f1\*sqrt((s1-46\*sin(c1)-34\*sin(c1+c2))^2+(y1-46\*cos(c1)-34.5\*cos(c1+c2))^2))^2)+...

4\*900/(900-(f2\*(46\*cos(c4+c5)+34\*cos(c6)+sqrt((s2-25-46\*cos(c4)-34\*cos(c4+c5))^2+(y2-46\*sin(c4)-34\*sin(c4+c5))^2))+f5\*sqrt((s5-25)^2+(y5)^2))^2)+...

4\*900/(900-(f2\*(34.5\*cos(c6)+sqrt((s2-25-46\*cos(c4)-34\*cos(c4+c5))^2+(y2-46\*sin(c4)-34\*sin(c4+c5))^2)))^2)+...

4\*900/(900-(f2\*sqrt((s2-46\*cos(c4)-34\*cos(c4+c5))^2+(y2--46\*sin(c4)-34.5\*sin(c4+c5))^2))^2);

结果为：

x =

Columns 1 through 12

39.2281   53.1696   19.8605   85.7515   69.5218   49.9037   23.8427   31.2546    0.6226   -1.3253   -0.0000    1.7621

Columns 13 through 23

\-1.0085   -1.3253    9.1429   48.6747   41.1023   23.2256   47.6912   24.2121   20.0389   31.3253    4.0050

f =

\-0.0202

smallestmoment =

\-0.0202