Minimization problem with constraint
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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 ?
采纳的回答
Alan Weiss
2018-9-13
0 个投票
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
更多回答（2 个）
Bruno Luong
2018-9-13
编辑：Bruno Luong
2018-9-13
Here is solution
R = -Inf
x = something between min(ai,bi),max(ai,bi)
y = something between min(ai,bi),max(ai,bi)
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