Minimization problem with constraint

Hello, the problem is as follows: Minimize R Subject to: (x-a_i)^2+(y-b_i)^2 ≤ R^2

Am looking to find x, y and R, knowing that

• a_i and b_i are known values from (100*1 matrices) each.
• x and y are within min and max of a_i and b_i.

Is it possible to find a solution with the optimzation tool of MATLAB? If not, any suggestion for a solution ?

Answer 1

[Alan Weiss]

I haven't tried this, but it sounds straightforward.

Decision variables: x(1) = x, x(2) = y, x(3) = R.

100 nonlinear inequality constraints: (x(1) - a(i))^2 + (x(2) - b(i))^2 - R^2 <= 0

Objective function: R = x(3)

Bounds: ll = min(min([a,b])), mm = max(max([a,b]))

lb = [ll,ll,0] , ub = [mm,mm,Inf]

Call fmincon from a reasonable start point, such as [(ll+mm)/2,(ll+mm)/2,abs(mm)]

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Bruno Luong]

Here is solution

R = -Inf
x = something between min(ai,bi),max(ai,bi)
y = something between min(ai,bi),max(ai,bi)

next

Answer 3

[Matt J]

You could probably use minboundcircle in this FEX distribution.