when i do fmincon live script optimize, the coordinate is different

i want to get a coordinate for maximum distance which form is

distance =10.361+0.40125.*a-0.34875.*c-0.78375.*a.*c

i plot this surface, and i saw (1,-1) is the best coordinate and the maximum distance is 11.8947

but when i do this for live script fmincon,

x0=[0 0]; 
lowerbound=[-1 -1]; 
upperbound =[1 1]; 

%objective function
function f = distance(x) ;
A=x(1); 
C=x(2); 
f= (-1).*(10.361+0.40125.*A-0.34875.*C-0.78375.*A.*C); 
end 
function [c ceq]=const(x) 
A=x(1); 
C=x(2); 
c=A+C-2; 
ceq=[]; 
end 

the answer is x=1 y=1 , not x=1 y=-1 that i saw by surface plot !!!!!! plz help me

in my picture, it says optimal point is x= 1, y=1

altough the coordinate is differant (1,1)=/ (1,-1)

result of maximum distance is same

[Matt J]

in my picture, it says optimal point is x= 1, y=1

It doesn't say that, as far as I can see.

Answer 1

[VINAYAK LUHA]

Hi Jong,

It is my understanding that the minimum coordinates on the surface plot subjected to the objective function calculated using “fmincon” function is different from the visually observed minimum coordinates. This is due to improper syntax of the used "fmincon" function.

Here's the corrected syntax to use to obtain the desired solution-

distance = @(x) -1 * (10.361 + 0.40125 * x(1) - 0.34875 * x(2) - 0.78375 * x(1) * x(2)); 

Since the bounds of the parameters is defined as below -

lb = [-1, -1]; 
ub = [1, 1]; 

This implies that x1+x2<=2, Which as per the documentation can be modelled as follows-

A     =[1,1]; 
b     = 2; 
Aeq   =[];
Beq   =[]; 
x0    =[0, 0]; 
x_min =fmincon(distance,x0,[1 1],2,[],[],lb,ub); 

Read through the below mentioned documentation on "fmincon" for more details

https://in.mathworks.com/help/optim/ug/fmincon.html#busog7r_sep_shared-A

Hope this helps!

Regards,

Vinayak Luha