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simple optimization problem
Posted:
Apr 13, 2012 2:44 AM


I want to solve the following simple optimisation problem with a mechanical background.
Given are two 2dimensional forces U_1 and U_2 acting on some rotor of length L.
I want to represent them as a composition of N other forces U_i at axial positions L_i of the rotor with 0 <= L_i <= L:
U_1 = 1 / L * sumoverN( ( L  L_i ) * U_i )
U_2 = 1 / L * sumoverN( L_i * U_i ).
The feasible sets for the forces U_i are some compact and convex polygons P_i.
I am interested in finding a solution for the forces U_i which minimizes for example the sum of their norms. But this is not my main concern.
My main interest is that the count of used forces U_i is as minimal as possible.
Has anyone an idea for realizing this?



