Questions tagged [dual]
The dual tag has no usage guidance.
13
questions
3
votes
0answers
50 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)
2
votes
1answer
113 views
Finding the dual problem of a minimum problem
How to convert the following primal problem into its dual problem:
\begin{align}
\min_{x,z}&\quad a^\top x + b^\top z\\\text{s.t.}&\quad Ax-d \le Cz \\&\quad x\ge 0, z \le 0.
\end{align}
I ...
3
votes
1answer
105 views
Electricity market clearing price using fixed-MIP formulation?
Dual information of electricity markets clearing problem is required to calculate the marginal clearing price. As most electricity market problems are based on MIP (and dual information of MIP is not ...
0
votes
1answer
726 views
Is optimal solution to dual not unique if optimal solution to the primal is degenerate?
If optimal solution to the primal is degenerate, does it necessarily follow that optimal solution to dual not unique? That is, is uniqueness an unnecessary assumption?
Spin-off from here.
In my ...
3
votes
1answer
209 views
Derive "true" shadow price for degenerated LPs using commercial solvers (e.g. Gurobi)
In linear programming for an optimal primal degenerate solution the values of the dual variables are in general not identical with the corresponding shadow prices. Several proposals on how to find the ...
2
votes
0answers
65 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}...
5
votes
1answer
188 views
Physical Interpretation of a dual of an LP
I was recently asked to physically interpret a dual of an LP for an audience who does not know mathematics/OR (without LP, dual, bounds, etc.). Though I attempted it and was very close to what the ...
2
votes
1answer
97 views
On dual-formulation of a given primal for a set-covering problem
I need to solve an LP-relaxation of an airline crew pairing optimization problem (CPOP). The problem formulation is a modified SCP and is as follows:
Primal of the CPOP:
\begin{align}\min&\quad\...
5
votes
1answer
130 views
Dual variables associated with same equation for different time instants
I have three equations that are essentially the same equation defined for three time instants. The equations are basically calculating the state of energy of an energy storage facility.
\begin{align}
...
3
votes
0answers
43 views
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 ...
7
votes
0answers
67 views
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);&...
9
votes
1answer
152 views
Finding Dual Objective
I have the following simplified optimization problem:
\begin{align}\max &\quad ax+by\\\text{s.t.}&\quad0 \le x \le \overline X\\&\quad0 \le y \le\overline Y\\&\quad z = E-x+\beta\cdot ...
18
votes
3answers
658 views
Column generation stabilisation
Has anyone performed a benchmark of the various stabilisation techniques in column generation? Which ones perform better for set pack/partition/cover problems like VRP? And are there theoretical ...
