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Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: simple optimization problem
Replies: 2   Last Post: Apr 14, 2012 1:37 AM

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Jürgen Womser-Schütz

Posts: 12
Registered: 12/13/04
simple optimization problem
Posted: Apr 13, 2012 2:44 AM
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I want to solve the following simple optimisation problem with a
mechanical background.

Given are two 2-dimensional 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?



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