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I have an optimization problem which is a multivariable problem(34 variables), I need to find the minimum cost but my solution must be only concerning to the value of 3 variables out of the 34; the other values must be zero. Concerning this problem the objective function is differentiable.

user3070616
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  • So it is an optimization problem in 3 variables with a differentiable objective function. There is really not much more to be said. – Johan Löfberg Sep 26 '14 at 17:28
  • The thing is that out of 34 variables any 3 of them can be considered. – user3070616 Sep 27 '14 at 06:10
  • Aha, I see. That is typically a nasty problem, but it can be cast using binary variables. Could you elaborate a bit on the objective function? – Johan Löfberg Sep 27 '14 at 06:38
  • the objective function in this case is a sumation of quadratic functions. 34 variables meaning 1 variable for each term of the sum in this case. – user3070616 Sep 27 '14 at 13:12

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If it is a sum of 34 separate quadratic functions $c_i x_i + q_i x^2_i$, the solution is most easily computed by minimizing each quadratic function individually (which you can do easily by setting gradient equal to 0), and pick the three variables corresponding to the three smallest costs. Or do you mean a sum of multivariate quadratics?

Johan Löfberg
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