# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
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### KKT conditions validation- one dual variable equating to two values

I have the following optimization problem: \begin{alignat}2\min &\quad A(t)\cdot x(t)-B(t)\cdot y(t)+C(t)\cdot z(t)-D(t)\cdot k(t)\\\text{s.t.}&\quad z(t)+z_1(t)-y(t)-y_1(t)+x(t) = k(t);&...
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### How to find the vectors to be added as the columns in the master problem of Dantzig-Wolfe Decomposition?

I have a Dantzig-Wolfe decomposition question with the following questions \begin{align} &Maximize: 2x_1 +3x_2+4x_3+2x_4 \\ s.t. \quad & x_1 +x_2+2x_3+x_4 \le 15\\ & x_1 +x_2+2x_3+...
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### Adding synchronisation constraint in Prize-collecting VRPTW

I am solving a Prize Collecting VRPTW. In my problem, each node represents a visit that needs to be made within a certain time window, and the "prize" for each node is the time spent at the ...
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### constrained optimization with decreasing constraint thresholds -Literature tips

consider a constrained optimization problem (typically c=0), with f highly nonlinear: $$\text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c$$ I experimented a bit and found ...
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### Constructive proof for the Hyperplane Separating Theorem (HST)?

HST is usually proven through the existence of a unique minimum-norm vector in a nonempty closed convex set. I think this is an existential proof. However, to actually apply the result in a real world ...
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