Unanswered Questions
63 questions with no upvoted or accepted answers
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
111
views
Dual instability, degeneracy, tailing off effect - Which are the causes and which are the effects?
Dual instability, degeneracy, and the tailing off effect are often mentioned together in papers. However, I cannot seem to find a clear explanation on which of these cause the other and vice versa? ...
- 173
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
237
views
Provide basic solution to CLP
I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
- 89
6
votes
0
answers
100
views
Proof that the leaving variable cannot be selected as the entering one in the next round
Using the Dantzig's pivoting rule, can it be proven that the leaving variable of one round cannot be selected as the entering variable in the next round?
6
votes
0
answers
107
views
Demonstrating a given solution is basic for a MCFP?
Given a minimum-cost flow problem, how could I go about demonstrating that a specific solution (as sets of basic and non-basic (!) arcs that build a rooted spanning tree for a given graph) is basic ...
- 253
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
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
165
views
All optimal solutions
I have a following problem:
If I have some function $aX+bY+cZ+mD+nF$ and I want to maximize it and have some constraints, how can I find ALL solutions for this maximum value of the function?
To sum ...
- 5,442
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
4
votes
0
answers
73
views
How can non-polyhedral sets be investigated?
To derive problem-specific cutting planes for some given problem (think something like TSP problem), one common way is to study small examples. To this end, one can create small instances for the ...
- 2,986
4
votes
0
answers
272
views
Does anyone have the criss cross algorithm programming code to solve linear programming problems?
I have a project that requires programming code for the simplex algorithm and criss-cross algorithm. The purpose of this project is to compare the two methods. I've tried to find it, but the ...
- 81