Unanswered Questions
95 questions with no upvoted or accepted answers
15
votes
1
answer
309
views
Integrality gap in bilevel binary linear programming problem
I have a bilevel max-min optimization problem over binary variables, with constraints expressed using linear inequalities. The inner (minimization) problem is
$$
\begin{alignat}2
\min\limits_x&\...
11
votes
0
answers
164
views
Characterizing the solution of a (non) linear maximization program
I have the following maximization program
\begin{align}
\max\limits_{\{q_i\}}&\quad\sum\limits_{i=1}^nq_i \\
\text{s.t.}&\quad\begin{cases} k_j \geq \sum\limits_{i=1}^n q_i^{1 \over \...
- 591
6
votes
0
answers
127
views
Water quality component optimization
I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
- 5,874
6
votes
0
answers
135
views
Characterization for total dual integrality
A problem I study reduces to whether the polyhedron $P=\{\mathbf{x}\mid A\mathbf{x}=\mathbf{1}, \mathbf{x}\geq0\}$ is integral ($A$ is a matrix with coefficients in $\{0,1\}$). I know that the ...
- 137
6
votes
0
answers
87
views
How to communicate number of integer combinations to a user
I'm working on a nifty little feature for our next release, i.e., to print the number of possible integer combinations left during branch and bound.
This is really handy for the user because they ...
- 5,442
6
votes
0
answers
125
views
Help in solving resource allocation optimization problem
I've been pondering on this question for some work optimization, and I need some help in being directed to the right direction.
I have multiple customers that require an amount of $X$, $Y$ and $Z$ ...
- 1,895
5
votes
0
answers
553
views
How to write this objective in CVXPY for quasiconvex programming?
I have the following objective that I want to maximize:
\begin{equation}
\max_{U_T\in \mathbb{R}, x\in\mathbb{R}^T} J_\alpha(U_T) = \frac{\alpha}{\alpha-1}\log\left(\frac{\cosh(U_T)}{\cosh(\alpha U_T)^...
- 86
5
votes
0
answers
89
views
Bounding the size of the dual solution
Given an primal optimization with bounded feasible set: $\max \{cx: Ax \leq b\}$.
The feasible region of the dual is $D = \{y:y^\top A = c^\top, y \geq 0\}$.
If the primal feasbile region is a ...
- 5,442
5
votes
0
answers
135
views
Is there a way to use lazy constraints with Baron?
I am solving a non-linear mixed-integer programme with BARON. The objective function looks like $\big( \sum_i x_i \big) \cdot \big(\prod_i e^{-y_i}\big)$ (binary $x$ and real-valued $y$) and it has ...
- 2,123
5
votes
0
answers
148
views
When is there at least an integral point in a polyhedron?
This problem comes from a problem of economics. Let $x\in [0,1]^n$. $\{x_1,x_2,\ldots,x_n\}$ is partitioned into ${S_1, S_2,\ldots,S_k}$ such that $\sum_{x_i\in S_j}x_i\leq 1$ for each $1\leq j\leq k$....
- 137
5
votes
0
answers
183
views
Are there any good models for min-max vehicle routing problem?
I am trying to model a min-max VRP problem with multiple delivery vehicles and I have come up with a model using branch and cut but I do not think it is strong enough as it takes lot of time to ...
- 253
5
votes
0
answers
44
views
In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples
Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion.
...
- 5,442
4
votes
0
answers
107
views
How to linearize or convexify a constraint with a square root of sum of two variables?
Here is the constraint:
$$\text{Pa} + \text{Pb}=a + b \sqrt{\text{Ir}^2 +\text{Ii}^2} + c (\text{Ir}^2 +\text{Ii}^2)$$
Here $\text{Pa}, \text{Pb}, \text{Ir},$ and $\text{Ii}$ are variables. $a, b, c$ ...
- 5,442
4
votes
0
answers
36
views
Does knowing the "correct multipliers" for globally optimal first-order critical points help you algorithmically?
Consider the following nonlinear optimization problem:
\begin{align*}
&\min f(x) \\
\text{such that } &h_1(x) = 0, \\
&h_2(x) = 0, \\
& \vdots \\
& h_m(x) = 0,
\end{align*}
where $...
- 1,895
4
votes
0
answers
288
views
Linearize a highly non-linear objective function
[EDIT] : The formula below is updated to remove the radical, 0.5 in the term $(I_{i,v} \cdot \Delta t)$ and constant temperature $T$ replces temperature as function of current.
[EDIT] :The values of ...
- 349