Questions tagged [dual]

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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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Derivations for two formulae for obtaining optimal dual variable values from the optimal primal tableau

We're being taught Industrial Engineering and Operations Research for the first time this semester. Referring to the book by Hamdy A. Taha, I noticed the mention of two formulae for swiftly obtaining ...
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Deriving KKT Conditions for time-step equations

I have a variable $e(h)$, and below is the part of the Lagrangian equation where I am taking the derivative with respect to $e(h)$. $$\frac{\partial }{\partial e(h)} \hspace{.2cm}\mu_1(h)(e(h)-\bar{E}...