All Questions
Tagged with linearization nonconvex-programming
9
questions
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
-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
109
views
using milp for a linear complementarity problem
I have to minimize $c^Tx$
subject to $Ax = b$, $x_iw_i = 0$ for all $i$, with $x$ non negative continuous and $w$ binary.
What model should I use to solve this problem?
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
4
votes
1
answer
599
views
How to linearize a non-convex optimization objective function?
The non-convex multi-objective optimization problem in my case is defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)+C_3X_1+C_4X_2+C_5(X_2^2/X_1)$
Objective 2: Minimize $...
- 179
1
vote
1
answer
229
views
Non-linear optimization local or global solution
In an NLP, I have a constraint that I would like to formulate in a convex manner preferably without introducing binary variables and/or big M formulations if possible. The actual problem is non-convex ...
- 81
4
votes
1
answer
435
views
Maximizing a piecewise-linear convex function
Note: Initially posted on MathOverflow.
I am working on an optimization problem where some of the terms of the objective function to maximize are expressed as a piecewise linear function of variables:...
- 141
6
votes
1
answer
251
views
Linearizing the square root of binary summations
My question is similar to this one and almost identical with this. I am so confused due to indexing and could not make sure if I could apply the solution in here to this indexed version as shown below....
- 1,249
7
votes
1
answer
102
views
Linearizing the square root of two binary summations
My question is similar to this one though a bit more complicated. Though my question also includes indices, I am removing them to ease readability.
Let binary variables $x,y\in\{0,1\}$, non-negative ...
- 1,249