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I define an optimization problem for the following scenario:

Let $S={V_1,...,V_L}$ be a set of real valued variables, defined in domain $\ [0,1]$.

I have constraints as follows.

1) I want sum of variables less than or equal to some given value $X$,

2) A subset of variables is defined as, $T\subset S$ where each member of $T$ must get values in interval like $[\epsilon,1]$

3) Rest of the variables in $S$ must be set to zero, i.e., $V_i=0, \forall i \in T^c$ where $T^c$:= $S$\{T}

Please note that I also want that the subset $T$ must contain some variables, i.e., $T\ne$ {}

I write following optimization problem for some maximization function $f_0$ as,$$\textrm{Maximize}\ f_0(V_i)\\ \textrm{subject to}\ \ \sum V_i \le X, \forall i \in S \ \ \ (1)\\ \epsilon\le V_i\le 1, \forall i \in T \ \ \ (2)\\ V_j=0, \forall j \in T^c \ \ \ (3)$$

I want to confirm whether the constraints 2 and 3 are defined correctly with respect to the constraints as I write in plain text as aforementioned?

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  • $\begingroup$ Your constraints look perfectly good to me. $\endgroup$
    – tomi
    Jan 9, 2017 at 11:17
  • $\begingroup$ Is $T$ a parameter? Do you want to solve it as a linear programming problem? $\endgroup$
    – LinAlg
    Jan 9, 2017 at 14:37

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