Questions tagged [linearization]
For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.
22
questions with no upvoted or accepted answers
4
votes
0
answers
274
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
3
votes
0
answers
112
views
From Quadratic to MILP?
I am playing around with some Quadratic Programs (QPs), and I want to check if my reasoning is right concerning a re-modeling from QP to MILP. So, let's consider the below QP:
(QP) $\min c^T x + x^T Q ...
- 1,208
3
votes
0
answers
119
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[...
3
votes
0
answers
86
views
Function approximation of a complex objective function
I would like to approximate the following objective function using a simpler function that can use be defined in gurobi.
\begin{equation}
\min_{I_{i,v}} \ \sum^{N_v}_{v}\sum^{TT_v}_{i} \ C_{loss,...
- 349
3
votes
0
answers
75
views
Linearization of a quadratic model, what is the difference while using gurobi?
I have a quadratic model of parking $N$ cars in $S$ separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ...
- 489
3
votes
0
answers
166
views
How to linearize a max min objective function?
Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables:
$\underset{x}\max \underset{y}\min dy$
Associated with the linear set of constraints and right ...
- 583
3
votes
0
answers
90
views
Linearization of the shifted copy of a function
Suppose in a model I have the expression $y_{1}(x) = 10 + 5 x^2$ where $x \in [0,20]$ is a continuous variable. In order to be able to use an MILP solver, I piecewise linearise $z_{1} = x^2$, by ...
- 2,180
3
votes
0
answers
62
views
Linearisation using SOS2
I am trying to linearise the following expresssion.
$C(k) = B(k) e^{-d(k)}, B(k) \ge 0 , d(k) \ge 0 $
I am trying to do this by using SOS2 sets.
I set $X(k) = e^{-d(k)}$ and I get $C(k) = B(k) X(...
- 2,180
2
votes
0
answers
88
views
The linearization of the logical constraints
I know the logical constraints can be linearized by either the logical representation of whose relation, (for pure binary variables e.g. CNF/DNF) or for general form by using Big-M formulation. As I ...
- 8,450
1
vote
0
answers
31
views
Moment based linearization of PDF for LP based optimization
Suppose I’m interested in modeling risk/volatility using the Cauchy distribution and I’d like to optimize some allocations using linear programming.
The Cauchy distribution is quadratic in nature but ...
- 501
1
vote
0
answers
51
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
$$
and $a_i, b_i, c_i$ are given. How to convert it into a ...
- 11
1
vote
0
answers
40
views
How to linearize a product and ratio of $x$ and $y$ where $x$ is binary and $y$ is a continuous variable?
I am an electrical engineer who is currently learning about optimization. From this post, they have shown how to linearize the product of two binary variables.
But in my case, I have a product $x \...
1
vote
0
answers
68
views
Linearization of Conditional Constraints for MIP using Cplex
I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
- 11
1
vote
1
answer
163
views
Nonlinear fractional objective function
Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally?
I only know that if the objective function has a single ...
1
vote
0
answers
81
views
Converting Nonlinear Program into an LP
I have a problem with a nonlinear objective function which is
\begin{align}\min&\quad Z_j\cdot(N_j)^{0.5}\end{align} where $j$ is the index.
I want to know how can I turn it into a linear ...
- 35
0
votes
1
answer
144
views
Production scheduling
I'm formulating a scheduling problem with the following decision variables:
$$X_t \space \text{is power sold to market in time period t} \\
Y_t \space \text{is power used for production in time period ...
0
votes
0
answers
28
views
Handling Variable Division in CVXPY for Calculating Annualized Rate of Change
I am working with a dataset that contains multiple entries for different IDs across various years. Some IDs might have a gap of years between entries. My goal is to solve an optimization problem using ...
- 101
0
votes
0
answers
75
views
Transforming a quadratic constraint into a linear constraint
I have a problem with a quadratic constraint and I want to transform it into a linear constraint. This would help to reduce the computational time of my problem.
Following constraint should be ...
- 11
0
votes
0
answers
76
views
Optimize revenue function with log part
I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function:
$$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
- 163
0
votes
1
answer
72
views
Interpret the formulation of a pricing model in crowdshipping
I am trying to run the pricing model from the paper "Designing pricing and compensation schemes by integrating matching and routing models for crowd-shipping systems" on python with Gurobi, ...
0
votes
0
answers
45
views
How to linearize such a constraint?
My original content was like this:
Assuming that server $k$ can only allocate corresponding computing functions to MU $i$ after receiving their tasks. Let
$$ y_{i,k,t} = \begin{cases} 1 & \text{if ...
- 1
0
votes
0
answers
68
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