All Questions
Tagged with linearization convex-optimization
12
questions
2
votes
1
answer
126
views
How to model the constraints of min and max in cvxpy
I have a continuous variable $x_{ij}\in[0,1]$ and I need to write the following constraint:
$$M_i-m_i+1\leq C_i$$ where $M_i=\max\{j: x_{ij}>0\}$ and $m_i=\min\{j: x_{ij}>0\}$
- 403
0
votes
1
answer
105
views
How to model this constraint in a better way?
I have a resource allocation problem. There are $M$ users and $N$ resources (machines).
One user can be assigned to multiple resources/machines.
But maximum $B$ machines can be activated at a time for ...
- 2,377
2
votes
1
answer
84
views
Is the linearization with first-order Taylor approximation correct?
I have a QP problem as
$\min \hspace{2mm} x^TQx-c^Tx$
here $x$ in binary
I want to transform it into a MILP by writing the objective function as
$\min \hspace{2mm} z-c^Tx$
and then adding a constraint
...
- 2,377
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
1
vote
0
answers
65
views
transform minimize weighted sum of absolute value into a linear optimization
For example, we have an optimization problem
$$
\min \sum_{i=1}^{n} |w_{i} - a_{i}| b_{i} \quad \text{s.t.} \quad \sum_{i=1}^{n} c_i w_i = 0
$$
and $a_i, b_i, c_i$ are given. How to convert it into a ...
- 11
-1
votes
1
answer
77
views
How to linearize the multiplication of variables and transform this into an MILP?
Let $C=10$, $U=50$
$P_c,c=1,\cdots,C$ and $\alpha_{u,c},u=1,\cdots,U,c=1,\cdots,C$ are optimization variables
$\alpha_{u,c}$ is binary
$\sigma_{u,c}$, $d_{u,c}$ are known parameters
$\min \sum_{c=1}^...
- 2,377
3
votes
1
answer
390
views
How to deal this L0 norm of a vector of L2 or L1 norms in objective?
I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=[{\bf a}_1\hspace{1mm} {\bf a}_2 \hspace{1mm} {\bf a}_3 \hspace{1mm} {\bf a}_4 \hspace{1mm} {\bf a}_5];$
Here, ${\bf a}_1$...
- 2,377
5
votes
1
answer
470
views
What is a good way to penalise LP relaxation?
I have a binary integer program. It is of a large size and the solver is taking longer time.
I am thinking of relaxing the binary integer variable and making it a continuous variable.
How can I ...
- 2,377
0
votes
1
answer
177
views
How to linearise this nonlinear constraint?
I have a constraint in the form
$\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$
where $x_{m,n}$ is binary variable
$t_u$ and $\beta_u$ are continuous optimization ...
- 2,377
1
vote
1
answer
696
views
How to transform this problem with logarithmic objective function into an approximated convex optimization problem?
I have an objective function as follows
$\underset{x_{m,n}}{\max}\hspace{1mm}\hspace{1mm}\sum_{m=1}^{M}\log_2\left(\frac{\sum_{n=1}^{N}(1-x_{m,n})\omega_{m,n}+z}{\sum_{n=1}^{N}x_{m,n}\omega_{m,n}}\...
- 2,377
3
votes
1
answer
244
views
How can I linearise this nonlinear proportional relation constraint?
My optimisation problem has a constraint in the form
\begin{equation}
\begin{array}{*{35}{l}}
\text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\...
- 2,377
2
votes
1
answer
99
views
How to model these constraints correctly
$W$ is a vector of $N$ complex elements.
$D$ is a binary variable
The requirements are:
when $D==1$, $L_{\min}\le ||W||_2^2\le L_{\max}$
and when $D==0$, $||W||_2^2=0$
I have formulated the following ...
- 2,377