Questions tagged [constraint]
For questions related to constraints, i.e. any restriction or relation a set of decision variables has to satisfy.
114
questions
3
votes
1answer
75 views
How to make following constraint a convex one?
I would like to write a constraint as follows, where $x,y>0$ are optimization variables, and $a,b,c,d,A$ are positive constants. How to make it a convex constraint?
\begin{equation}
\frac{{ax}}{{\...
2
votes
1answer
64 views
CPLEX Indicator Constraints in Java API
I'm using the Java API of CPLEX (12.6.1 version) to solve a MILP problem.
This is how I create 'normal' constraints:
...
0
votes
1answer
45 views
How to create constraint-equations in Pyomo with empty set inputs
I would like to crate an constraint-equation that depends on 4 sets. For that I use the following code:
...
6
votes
1answer
132 views
Two equivalent soft constraint implementations
Take the following optimization problem:
\begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g(x)\le0\end{align}
with $f$ and $g$ nonlinear functions. Suppose I want to relax the constraint by ...
1
vote
2answers
92 views
Show the total unimodularity of constraints matrix
I have a model as below.
I have constructed the matrix of its constraints as below. I need to show the total unimodularity of its constraints matrix. However, the determinant of the below submatrix (...
2
votes
3answers
75 views
Convex optimization on the unit hypercube with gradients and a bounded minimum
I'd like to find the minimum of a smooth, continuous function inside the unit hypercube (the dimensionality of which could go into the hundreds or even thousands). The function is convex (Hessian $\...
4
votes
3answers
126 views
How to couple a binary variable to a continuous variable to indicate values greater 0
I have a continuous variable $x_t$. A binary variable $b_t$ should be coupled to $x_t$ such that $b_t$ has the value $1$ if $x_t$ has a value greater than $0$ and $b_t$ has the value $0$ if $x_t$ has ...
5
votes
1answer
206 views
How to set a limit for a switch to 0 of a variable for 2 variables combined
I have a follow up question to another question of mine How to set a limit for a switch to 0 of a variable about counting the number of switches to 0 of one decision variable. Now I would like to ask ...
4
votes
1answer
305 views
Is there any automatic way to spot contradictory constraints in linear programming?
Let's have the following trivial linear program: \begin{align}\max&\quad z=20A+30B\\\text{s.t.}&\quad A\le60\\&\quad B\le50\\&\quad A+2B\ge220\\&\quad A,B\ge0\end{align}
It's easy ...
2
votes
1answer
38 views
How to write the following constraint? [duplicate]
I would like to write the following constraint, where $varBuyWater$ and $varSellWater$ are decision variables on how much water to buy and to sell. However, I do not want the solver to buy and sell ...
5
votes
1answer
190 views
How to set a limit for a switch to 0 of a variable
I would like to know how to define a constraint to set a limit for switching to 0 for a decision variable? So I have a linear variable $x(t)$ which quantifies the modulation degree of a heating device....
2
votes
1answer
52 views
Constraints that set values to binary variables depending on other binaries
I am trying to write a mathematical problem that involves some conditions based on binary variables. More specifically, I have a set of three binary variables $d_1$, $d_2$, $d_3$ and depending on ...
3
votes
1answer
186 views
How to find out which constraint causes problems in Pyomo
I have a Pyomo model with many constraints and variables. When solving it with Gurobi, I get the message "Model is infeasible or unbounded". Now I would like to find out which constraints ...
0
votes
0answers
118 views
Use if-statements when defining a constraint in Pyomo
I would like to define the value of a variable model.variable_costsPerTimeSlot [t] in pyomo and I would like to use if-statements. Depending on the value of the if-...
1
vote
1answer
29 views
How to assure a range for a specific variable in Pyomo
I would like to specify a certain range for a variable for a certain timeslot in Pyomo. I have a temperature variable $T(t)$ that is defined by using the difference equation $$T(t) = T(t-1) + \cdots,\...
2
votes
1answer
29 views
Piecewise Constraint in Abstract Model
I would like to write a piecewise constraint for an Abstract Model in Pyomo.
$$\operatorname{pu}_i(t_i^{'v})=\begin{align}\begin{cases}\rho_1(e_i'-t_i^{'v})+\rho_2(e_i-e_i'),\quad& t_i^{'v}\le e_i'...
0
votes
0answers
23 views
Correct way to define constraints in Pyomo
Can I know if the constraint below can be defined as follows in Pyomo for convex optimization.
W and G are arrays of dimension M x N.
...
1
vote
1answer
45 views
Can I define constraints in Pyomo as a list?
I would like to define the following constraint in Pyomo $$W^\top{\bf 1}\le\hat w=\begin{bmatrix}\hat{w}_1&\hat{w}_2&\ldots&\hat{w}_N\end{bmatrix}^\top$$ where $W$ is a $2\times4$ matrix. ...
6
votes
2answers
157 views
Index of element in MILP vector decision variable that equals 1
Consider a decision variable in a MILP constrained:
$$\sum_i p_i = 1$$
$$p_i\ \in \{0, 1\}$$
Obviously one element in $p$ is 1 and all others are 0. How can I set a decision variable to the index i of ...
2
votes
1answer
128 views
Matrix Singularity Constraint
I'm using CVXPY. Given a $2\times2$ matrix $A$, is it possible to add a singularity constraint?
Anything equivalent to:
$|A| = 0$: The determinant is $0$
$\operatorname{rank}(A) \leq 1$
Smallest ...
1
vote
1answer
121 views
MILP constrained by the minimum number of satisfied constraints
I have an MILP where we have
$$
t_k = \sum_i P_i\cdot C_{ik} : P_i\ \in \{0,1\}, C_{ik} \in I^+
$$
and our model is constrained by the number of times $t_k$ is bigger than a certain value $T_k$.
$$
\...
3
votes
1answer
98 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:...
4
votes
2answers
428 views
Modeling a constraint such that a set of binary decision variables do not equate to 1 simultaneously
I would like to seek some advice on modeling the following logical condition:
I would like to ensure that a group of binary variables do not equate to 1 simultaneously, i.e., $\omega_{1}=1, \omega_{2}=...
3
votes
1answer
91 views
Linearize $\max x_i\ge1$
I'm trying to linearize this optimization problem ($S_j$ is a subset of variables): \begin{align}\min&\quad\sum_{x_i \in X} x_i\\\text{s.t.}&\quad\max_{i \in S_j}x_i\geq 1\quad\forall S_j\\&...
3
votes
0answers
99 views
Two binding constraints - Linear Programming
I'm having some troubles to continue solving my system, I'm used to solve such systems but with "one" binding constraint, if someone could give me some helpful hints so I can solve it I will ...
2
votes
2answers
301 views
If-then constraint with continuous variables
I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the ...
1
vote
2answers
98 views
Should I process the data or add a new constraint to achieve the target?
I have an MILP as below
$\begin{equation}
\begin{array}{*{35}{l}}
\underset{d_{u,c}}{\max}\hspace{1mm}\hspace{1mm}\sum_{u=1}^{U}\sum_{c=1}^{C}d_{u,c}\omega_{u,c}\\
\text{}\text{subject to }\text{ C1:}...
2
votes
1answer
86 views
How to define constraints in Pyomo using sets and variables
I am trying to model the transportation problem of Dantzig in Pyomo (see the GAMS code here https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_trnsport.html or the description here https://www....
2
votes
2answers
250 views
Hard to soft constraint
What are all necessary changes to the below model so that constraint set $(2)$ becomes soft?
Give the new full model. $\alpha_{ij}$ are parameters. Eqn. $(1)$ refers to an already existing function of ...
2
votes
0answers
71 views
How to linearize this multiplicative constraint?
I have a constraint in the form
$\sqrt{|\sum_{c\in C}{h_cw_c}|^2}\ge\sqrt{x}\zeta$
Here, $h_c$ is s row vector (know), $w_c$ is a column vector (variable).
$x$ and $\zeta$ are also optimization ...
2
votes
1answer
68 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
votes
2answers
101 views
Constraint to handle the machine-configuration's change between initial position and its first occurrence in the process
I am working with a kind of a reconfigurable process planning, meaning that the same machine can have different configurations and perform multiple operations. Each machine has an initial ...
1
vote
1answer
55 views
Priority Constraint
Suppose I have the following set of binary variables:
$X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$
$Y_j$: $J$ ranges from {1,..,3}
$Z_k$: $K$ ranges ...
2
votes
1answer
109 views
How can I perform discrete optimisation of a variable over a data set
This question relates directly to a dataset I've generated for Fantasy Premier League, but I'm also curious how I can apply this to a more general case.
Data
I have a list of premier league players, ...
1
vote
1answer
176 views
Python, Google OR-Tools, OnlyEnforceIf() method
I am trying to solve a basic puzzle by using Google OR-Tools, this is my first try with OR-Tools and I am trying to learn. I completed almost everything and was ready to conclude the program until I ...
3
votes
3answers
202 views
How to handle an equality constraint in metaheuristic algorithms (like GA, PSO)?
Metaheuristic algorithms are generally used to find the optimal solution to unconstrained optimization problems. I would like to maximize $x_1+3x_2-x_3\ge0$ while respecting the equality constraint $...
5
votes
0answers
223 views
Substituting inequality by equality constraints
Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row or column has all its entries equal to zero. Let also $\mathbf{k}=\left(k_j\right)$ be a ...
4
votes
1answer
64 views
How do you turn an abstract set constraint into equality constraints?
I am reading from Nonlinear Programming by Bertsekas, and in the section on ADMM, he says:
Consider the problem
$$\text{min} \sum _{i=1} ^ m f_i(x)$$
$$\text{s.t. }x \in \cap _{i = 1}^m X_i,$$
where $...
5
votes
2answers
319 views
Failing to meet a constraint in a NLP problem
I have a NLP problem at hand, which I am trying to solve via Pyomo + ipopt. I try to run several different instances of the optimizer with different conditions, out ...
8
votes
1answer
427 views
Adding a constraint in constraint programming
Is it true that the more we add constraint to a constraint programming solver the more efficient it will be? How does this compare to adding constraints in integer programming solvers.
5
votes
1answer
84 views
Combined arc capacity constraints in network flows
Consider the network flow polyhedron for a directed graph $G = (N, A)$. Along with the standard flow-balance and single-arc capacity constraints, we are faced with additional constraints which enforce ...
0
votes
0answers
39 views
Linearizing max constraint Problem [duplicate]
I want to linearize a max constraint as below:
In which x_(i,t),are binary decision variables and T is a constant.
How can I linearize this constraint?
2
votes
1answer
60 views
distance specific constraint
I have some points with determined coordinates $(a_i,b_i)$. A vehicle can move between these points based on rectangular distance. In more detail, we consider that the path between points is an ...
3
votes
2answers
171 views
Model “If, then” constraint
How to model the following "If, then" type constraint?
If $\sum\limits_{i \in I}x_i = 0$ then $\sum\limits_{j \in J}x_{j} = n$
where $x$ are binary variables, $n$ is a known parameter and $...
2
votes
1answer
65 views
Quasi-convex function must be “partially monotonic”?
$f(x)$ is quasi-convex,
$$x^*\in\arg\min_{x\in C}f(x).$$
How to prove that, for any $a\in C$, $f(x) $ is weakly monotonic in the direction of $(x^*-a)$?
Is this simple result a part of an ancient ...
4
votes
3answers
200 views
Faster implementation of “or” constraints in ILP
I have implemented a set of "or" constraints in my ILP using binary decision variables (as in this method). It works fine for smaller problems, but when I try to increase the number of ...
5
votes
1answer
106 views
Minimize binary variable's distance with respect to the index values
For a given binary decision variable $x[i,j,k]$ my goal is to get as dense results in terms of k for successive values of j. Distance of k value to be kept as close as possible throughout j values:
$d ...
3
votes
3answers
237 views
Possibility of indexing decision variables with 2 indices using a set of tuples in Pyomo
I am currently attempting to solve a network problem that is not fully connected.Thus, I have attempted to do some preprocessing of data so as to form a set of tuples, e.g. $\{(a,b), (c,e),\ldots\}$, ...
3
votes
1answer
183 views
View of Constraints and Decision Variables in Pyomo
I have just attempted to construct my first Pyomo model.
However, I was unable to locate any documentation that shows how to view constraints, decision variables.
As my model is big, I need to see ...
3
votes
3answers
317 views
SLSQP Optimisation loop takes several iterations to compute error function despite jacobian
I have an error function $f : w \rightarrow f(w)$ that I want to minimize, $w$ being a vector of length 211. There are some constraints on $w$.
I managed to compute the jacobian $J$ and even with it ...
