# Questions tagged [karush-kuhn-tucker]

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions are first order necessary conditions for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.

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### Analytical derivation of linear optimization problem with KKT conditions possible at all?

I would like to find an analytical solution to a linear optimization problem optimizinig over multiple time steps. Following a reduced version of the LP with variables denoted in capital letters and ...
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### Tucker Nearness Problem

I'm still not very confident with tensor calculus and I came across a paper that was solving an optimization problem based on Tucker decomposition; I don't understand how, from the initial formulation,...
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### Which decision variables to consider in the KKT transformation of a bilevel optimization problem into a single-level one when collocation is used?

I am currently dealing with a dynamic bilevel optimization problem, that is, the variables are changing in time as described here: general problem formulation. To address the dynamics of the system, ...
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### How to minimize $x$ subject to $y \le x^3$ and $y \ge 0$

I have been getting into NLP, the Karush Kuhn Tucker theorem and the Linear Independence Constraint Qualification and I came across this problem. My first attempt was to solve graphically and I ...
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### One dimensional constrained optimization: KKT conditions versus irregular points

In a constrained optimization problem, we search local solutions in the regular points that satisfy the KKT solutions as well as the irregular points. All the local solutions are included in these ...
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### Necessity of non negativity conditions of slack variable in KKT

I have the following question: $\min \frac{1}{2}w\cdot w + \frac{C}{2}\sum_i\xi_i^2$ subject to $y_i(w\cdot x_i + b)\ge1-\xi_i \; \; \forall i$ Where $\xi_i$ are slack variables. Show that the ...
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