Global Optimization in Chebfun3
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Georgy Scholten
Jun 1, 2024, 1:07:48 PM6/1/24
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Dear All
I would like to know if there is a way to compute all local minima of a Chebfun3 object over (-1,1)^3.
I see two ways of going about it:
1) Compute all critical points of the object, in that case, I am trying to solve a polynomial system of the form:
P1(x, y, z) = P2(x, y, z) = P3(x, y, z) = 0, where each P_i is encoded as a chebfun3 object.
Let's assume we know ahead of time the system has finitely many solutions. I am under the impression that root function does only return a single solution to the system.
Would solving the polynomial system by a homotopy method could be conceivable in this case?
2) Maybe there already exists some iterative approach, using the max3 function for instance?
All the best
I would like to know if there is a way to compute all local minima of a Chebfun3 object over (-1,1)^3.
I see two ways of going about it:
1) Compute all critical points of the object, in that case, I am trying to solve a polynomial system of the form:
P1(x, y, z) = P2(x, y, z) = P3(x, y, z) = 0, where each P_i is encoded as a chebfun3 object.
Let's assume we know ahead of time the system has finitely many solutions. I am under the impression that root function does only return a single solution to the system.
Would solving the polynomial system by a homotopy method could be conceivable in this case?
2) Maybe there already exists some iterative approach, using the max3 function for instance?
All the best
Georgy Scholten
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