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I have an optimization problem formulated as follows. Let optimization function be defined as:

maximize $\sum_j \sum_w f(𝑥_{𝑤,𝑗}\cdot \mbox{𝑐𝑜𝑛𝑠𝑡}) + g(𝑥_{𝑤,𝑗})$

subject to: $\sum_w 𝑥_{𝑤,𝑗}\cdot 𝑦_{𝑗,𝑚} \cdot 𝑂_{𝑤,𝑗} \leq 𝑇_𝑗 \left(\forall 𝑗, \forall 𝑚\right)$

is a binary valued decision variables.

Both $f(x)$ and $g(x)$ are linear functions and constraint is also linear but unfortunately decision variable $x_{w,j}$ is binary valued.

I am confused if I can use interior-point method to solve it?

Thanks,

raza

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Interior point methods are for continuous LPs (and related problems). They could be used to solve relaxations inside a branch-and-bound framework. However often Simplex is used there because it has better capabilities to continue from a previous point (or rather basis in LP terminology).

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