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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);&...
S_Scouse's user avatar
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3 votes
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134 views

How to find robust counterpart of sum of logit functions?

Suppose function $\mu_i(y):\mathbb{R} \rightarrow \mathbb{R}$ is a logit function, $\mu_i(y)=1/(1+\exp(-y))$. Also, we assume that $\mathbf{x}_i\in \mathbb{R}^d$ and $\theta \in \mathbb{R}^d$. I am ...
Amin's user avatar
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3 votes
0 answers
67 views

Dual of the alternative solutions

Suppose we have two alternative solutions for a linear program. Are their corresponding dual solutions the same? (in terms of the values for each dual variable)
Junior MIP's user avatar
3 votes
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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 ...
Sakazuki Akainu's user avatar
2 votes
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70 views

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}...
S_Scouse's user avatar
  • 803
1 vote
0 answers
67 views

Dual of a quadratic constraint

This is my model. \begin{align} \min_x&\quad\sum_{e\in E} X_e p_e \\ \text{s.t.}&\quad\sum_{e \in E: T(e)=i} X_e - \sum_{e \in E: H(e)=i} X_e = \begin{cases}1, \;\text{if}\;i=s\\-1,\;\text{if}...
orpanter's user avatar
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Dual of a LP with a variable restricted to be negative

I have to find the dual of following LP: Minimize $ x_1 + x_2 + x_3$ subject to $4x_1 + 8x_2 \geq3$ $7x_2 + 4x_3 \leq 6$ $3x_1 - 2x_2 + 5x_3 = 7$ $x_1 \leq 0, x_2 \geq 0, x_3$ is unrestricted I ...
A Y's user avatar
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