All Questions
Tagged with linearization nonlinear-programming
38
questions
2
votes
2
answers
184
views
Are McCormick Envelopes exact for the following class of optimization problems?
I have the following optimization problem:
\begin{align*}
\text{minimize} \quad &\mathbf{c^T x} \\
\text{such that} \quad &\mathbf{x} \in S.
\end{align*}
Here, $S$ is a polyhedron of the form $...
- 205
1
vote
1
answer
45
views
Converting a function composing of multipe pieces into a linear equation
I have a variable (alpha) which depends on some other binary variables, denoted as X_i. So, for some combination of other variables, alpha may take a value (Beta_j). I added some auxillary variables (...
- 97
2
votes
1
answer
216
views
How to transform a binary QP into an MILP?
I have a binary quadratic problem with objective ${\bf{x}}^T{\bf{Qx}}+{\bf{c}}^T{\bf{x}}$
subject to
${\bf{A}}{\bf{x}}\le{\bf{b}}$
${\bf{A}}_{eq}{\bf{x}}={\bf{b}}_{eq}$.
here ${\bf{x}}$ is binary.
...
- 2,377
0
votes
0
answers
58
views
Better formulation of bilinear terms
I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
- 23
1
vote
1
answer
58
views
$\min\{f(x_1),\dots,f(x_n)\}$ with other constraints
I have an optimization problem which goes:
\begin{align*}
\text{Minimize:}
\\
& \sqrt{x} + \sqrt{y} \tag{NL-objective}
\\
\text{Subject to:}
\\
&3x + 2y \geq 2 &...
- 11
0
votes
0
answers
72
views
Resource selection problem with non-linear objective function
I have an optimisation problem to solve but I can't model it correctly. Any insight is welcome :)
It has been a few years since my optimisation classes in university, and while I have forgotten a lot ...
- 1
2
votes
3
answers
230
views
Linearization the product of three variables (two binary & one continuous)
Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$.
I am trying to model the following conditional equations as constraints:
\begin{cases}
...
- 113
1
vote
2
answers
224
views
Nonlinear fractional objective function
Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally?
I only know that if the objective function has a single ...
4
votes
1
answer
185
views
How to solve a "nearly" linear program
Given a positive integer $n$, a constant $k=2/3$, and $7$ variables $x_1, x_2, x_3, x_{12}, x_{13}, x_{23}, x_{123}$ (non-negative reals or integers) I would like to find:
$$\min \binom{x_1}2$$
...
- 393
3
votes
0
answers
153
views
Linearize objective function with non-linear terms
I have a problem with linear constraints but in the objective function I want to have some linear terms along with a $x^2$ term. So it is like the following:
$$\min \sum \limits _i \sum \limits _j (a[...
2
votes
1
answer
138
views
Lifting a 3rd order polynomial into a higher dimensional space
An MINLP from a paper I am reading has the following expression in its constraints:
$$
p_{l,s}=z_lb_l\Delta\theta_{l,s}+b_l\lambda_{l,s}u_l\Delta\theta_{l,s}
$$
Where from left to right:
$p_{l,s}$: ...
- 113
5
votes
2
answers
584
views
Transform nonlinear cost function to get LP or MILP
I'm trying to schedule power of multiple prosumers in a microgrid.
The problem includes a cost function with min and max ...
- 153
2
votes
2
answers
243
views
Difference between constraint formulation and performance
I am wondering about the characteristics and performance of some constraints with only binary variables. I assume that solving (integer) linear programs is faster than quadratic ones.
At first:
$$
a,b,...
- 147
1
vote
1
answer
85
views
If $x=\min\{f(\mathbf{a}),1-\epsilon\}$, how can we model and partition $x$?
I have been dealing with a problem for sometime and although tried different things and asked some questions before, I think the problem might be somewhere that we didn't look before.
Variables $0\le ...
user9659
2
votes
1
answer
74
views
Linearizing $y=\sum_{i=1}^n(z+c)\left(\frac{r_i^2}{1-r_i}\right)\phi_i$
Variables $0\le x< 1$, $y,z\ge 0$. We have a constraint
$$y=(z+c)\frac{x^2}{1-x},$$
where constant $c>0$.
We partitioned $x$ into $n$ intervals of equal length and defined a new variable $\phi_i=...
user9659