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Questions tagged [constraint]

For questions related to constraints, i.e. any restriction or relation a set of decision variables has to satisfy.

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How to linearize a chain of if-then constraints?

How can I express the process of converting a series of if-then constraints into a linear form? Let's assume that we have integer variable $x_i$, non-negative variables $y_i^d$, and binary variables $\...
linkho's user avatar
  • 175
4 votes
2 answers
348 views

union of constraints

How to solve problems like $\min_x f(x) \\ g(x) < 0 \ or \ h(x)<0$? I think we can solve $\min_x f(x) \\ g(x) < 0 $ and $\min_x f(x) \\ h(x) < 0 $, then we compare the solutions from these ...
StupidMan's user avatar
1 vote
2 answers
71 views

Grouping variables to take same value

Assume we have 50 variables that we want to split into 3 groups and each group should have at least 5 variables. How to formulate that all variables in the same group take the same values? I used the ...
milad's user avatar
  • 21
1 vote
2 answers
146 views

how to satisfy time constraints with meeting points?

I have a specific pickup and delivery problem to work on and am thinking how to incorporate time windows effectively. The problem has some driver with some time window [$a_d, b_d$] which is the start ...
Hemfri's user avatar
  • 11
3 votes
0 answers
54 views

constrained optimization with decreasing constraint thresholds -Literature tips

consider a constrained optimization problem (typically c=0), with f highly nonlinear: \begin{equation} \text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c \end{equation} I experimented a bit and found ...
Lukas Schroth's user avatar
2 votes
1 answer
164 views

it is possible to have a constraint that does not contain any decision variables

I had formulated an optimization model, and along the way I had to change a variable into a parameter. In doing so, one of my constraints that contained the variable I changed no longer contained a ...
orion's user avatar
  • 23
1 vote
1 answer
108 views

Sigmoidal programming

I plan to use sigmoidal programming from the git repo https://github.com/madeleineudell/SigmoidalProgramming.jl There are some issues with the implementation of this repo. It requires me to pass $A, b,...
Meet Saiya's user avatar
3 votes
2 answers
330 views

How to model this binary constraint?

I have an optimization problem that has a variable in the matrix form. The variable is a binary matrix. It has size $M \times N = 10 \times 50$ where $M$ is the number of machines and $N$ is the ...
TheExerminate's user avatar
2 votes
2 answers
349 views

Representing "and"/"or" relationships into constraints

How do I represent the following constraints in terms of equations? For each i, either (1) holds or (2) holds- $$ x_{1}^i \geq x_{2}^i \quad and \quad x_{3}^i \geq x_{4}^i \quad {(1)} $$ $$ x_{1}^i \...
T_k's user avatar
  • 77
3 votes
3 answers
214 views

Equivalence between constraints in ILP

Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that $$ z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$ If I wanted to express the equivalence between ...
tomashauser's user avatar
1 vote
1 answer
118 views

Linearize conditional constraint

Consider a variable c from the domain {-1,0,1}. I have the following constraint: IF $c = 1 \Rightarrow x = 1 $ ELSE $x = 0$ How do I linearize this constraint?
Waldo's user avatar
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1 vote
0 answers
51 views

How to speed up state of charge constraint in Pyomo model

Context: I am working on a small electricity market model in Pyomo. It optimizes the capacity of different technologies and generation in at least 43800 hours. One of the technologies is a battery. ...
funkypenguin's user avatar
2 votes
2 answers
48 views

How to restrict the amount of consecutive assignments

I'm working on a scheduling/rostering problem. In this scenario the shifts are predefined with a starting and ending date and time. The problem basically assigns people to shifts with a binary ...
Daniel Baquero's user avatar
0 votes
1 answer
57 views

Maximization problem with preferences on variables

Consider the following trivial, theoretical model: $$ \max x+2y+3z \qquad s.t. $$ $$ x \leq b_x $$ $$ y \leq b_y $$ $$ z \leq b_z $$ $$ x+y+z = 1 $$ $$ x,y,z \in \{0, 1\} $$ and $b_x$, $b_y$ and $b_z$ ...
Libra's user avatar
  • 927
1 vote
1 answer
63 views

Multiplicity-Constraint in Constraint Programming Solvers

I need to solve a CSP with a constraint imposing upper bounds on the multiplicity of variables in a list. More precisely, I need a constraint of the form ...
guigux's user avatar
  • 113
0 votes
1 answer
76 views

Meaning difference between SUMMATION and not in the MIP model

I'm asking you a question because I was confused about MIP while reading the paper. This paper is about dual crane optimization. In the MIP model of the paper, equations (7) and (8) are used to model ...
Kim's user avatar
  • 1
2 votes
3 answers
109 views

Efficient formulation of flexible job-shop scheduling constraints

I am working on a flexible job-shop scheduling problem, where indices are as follows: $i$: Index of operations $j$: Index of jobs $m$: Index of machines $p$: Index of operation sequences on a machine ...
mdslt's user avatar
  • 529
4 votes
2 answers
206 views

how to ensure minimum output of a generator (else zero output) in linear programming?

I want to ensure, that a generator (in my case a heat generator, for example a boiler) first starts to output thermal energy, when a certain minimum output can be realized. Otherwise the output should ...
Andre's user avatar
  • 293
3 votes
3 answers
278 views

Set null the next set of N values

I'm dealing with a problem I already modelled by using linear programming. The already existing constraints set at 1 groups of contiguous variables (for ex: ...
devOn's user avatar
  • 33
3 votes
2 answers
450 views

Binary integer programming with dynamic costs and total resource constraint

I am trying to find a suitable paradigm under which my discrete optimisation problem falls into. This looks similar to integer programming, so the goal is to find a binary vector $\bar{x}$. However, ...
shiftyscales's user avatar
2 votes
1 answer
69 views

Prove MF-Constraint Qualification but not LICQ is satisfied

Let $g_1(x):=(x_1-1)^2+(x_2-1)^2-2\leq 0, g_2(x):=(x_1-1)^2+(x_2+1)^2-2\leq 0, g_3(x):=-x_1\leq 0$ be given constraints. Show that the Mangasarian-Fromovitz Constraint Qualification (MFCQ) is ...
Uhmm's user avatar
  • 123
2 votes
1 answer
120 views

Piecewise constraint using big-M notation

I have a piecewise constraint that I am having a hard time converting using big-M modelling. The context is a gym owner that is updating membership costs subject to churn restrictions. The owner can ...
akkha's user avatar
  • 43
2 votes
1 answer
86 views

Formulate revenue maximization problem and find an appropriate solver

I am trying to maximize expected revenue over a horizon. Consider the following function: \begin{align} sales(budget_1, budget_2) = \sum_te^{C_1t} * budget_1t^{saturation_1t} + e^{C_2t} * budget_2t^{...
jakobhellander's user avatar
1 vote
1 answer
62 views

Problem to construct constaints in SAA method

Pop-Donuts located in Los Angeles of California makes two products, donuts and cakes. Pop-Donuts has bottlenecks in its capital used to purchase flour that is required in making both donuts and cakes, ...
falamiw's user avatar
  • 157
-2 votes
2 answers
57 views

How to model the following "if, then" constraint

There are two matrices: Matrix $S^{v\times v} \in \{0,1\}$ this is a know parameter. Matrix $X^{v\times p} \in \mathbb{N}$. Elements of $X$ are the variables. I want to model: $$\textrm{if }s_{v v'} =...
Daniel Baquero's user avatar
1 vote
1 answer
64 views

Homework Problem – Help Formulating Constraints [closed]

I am working on the following assignment problem: You may produce seven products by consuming three materials. The unit sales price and material consumption of each product are listed in Table 1. For ...
SDH's user avatar
  • 11
1 vote
2 answers
115 views

How to formulate this NLP problem correctly?

Current status on the problem (what I've done) I'm working on a NLP problem and I got a formulation of the problem, together with the necessary constraints, but I think it needs some adjustments to ...
Steven01123581321's user avatar
2 votes
1 answer
437 views

Optimization problem with if condition as constraint

I am trying to solve an optimization problem where the constraint contains absolute values and I am not sure how I can express this in a 'Pyomo-friendly' way. Consider the following optimization ...
BenBernke's user avatar
  • 175
3 votes
2 answers
379 views

Constrained optimization of a sum

I have to maximize the function $f= \sum_{i=1}^na_ix_i $ subject to the constraints $g = \sum_{i=1}^n x_i = 0 $, $-1\leq x_i \leq 1$ and $a_i>0$. Lagrange multiplier method doesn't work because $\...
Deep's user avatar
  • 133
3 votes
1 answer
265 views

Binary variables constraint

What constraints would you write to ensure that if $x = 1$ then $y = 0$ where $x, y$ are binary variables? Until now I only learnt how to build the constraint with 3 binary variables, therefore the ...
Bohdana Nevierova's user avatar
4 votes
1 answer
183 views

Difficult linearization of a constraint

My previous question was about this ILP with all binary variables: $$\min \sum_{1\leq i<j\leq n-1-h} t_{i,j}$$ $$\sum_{i=1}^{n-1-h} a_{k,i} = \lfloor (n-1)/2\rfloor \qquad \text{for }k\in[h];$$ $$...
BillyJoe's user avatar
  • 393
3 votes
3 answers
542 views

Gurobi - Python: is there a way to express "OR" in a constraint?

I'm new to Gurobi in Python and I am wondering if there is way to express/code "or" in the following constraint, where $x_i$ are binary variables: $x_i-x_i*x_{i-1} =0$ OR $x_i*x_{i+1} =1.$ ...
M.Badaoui's user avatar
  • 185
1 vote
1 answer
68 views

Can I get value from a variable and use it on a specific index of a different variable?

This is a peculiar question but I have two variables $s_{ik}$ (integer) and $y_{it}$ (binary). What I want is the following relationship: If $s_{ik} = 8$, then $y_{i8} = 1$. Basically, if $s_{ik}$ ...
arvind rathore's user avatar
3 votes
1 answer
122 views

Efficient modelling via Gurobi

I would like to model the following constraint set in gurobi-java. \begin{equation} t^n_{ij} \geq t^n_{(i-1)j}+S_{(i-1)j} - (1 - \sum_{\substack{m \in \mathcal{M} \\ G_{ijm} = 1}}\sum_{k \in \mathcal{...
mdslt's user avatar
  • 529
3 votes
1 answer
90 views

Projection to sublevel sets of convex/strongly convex function

Given a convex compact set $K\subset\mathbb{R}^D$ and convex function $f:K\rightarrow \mathbb{R}$, the sublevel set $$ X_\alpha = \{ x \in K : f(x) \leq \alpha \} $$ defines a convex closed set (...
ntrstd11's user avatar
  • 235
3 votes
0 answers
67 views

Projected Gradient Ascent for linear programming

I need to find a reasonable maximum for a linear programming problem, for which standard solvers for linear programming are just too slow. I was thinking of using projected gradient ascent, but do not ...
Carol Eisen's user avatar
3 votes
1 answer
274 views

Gurobi - Python: is there a way to express "for some" in a constraint?

I'm new to Gurobi in Python and I am wondering if there is way to express/code "for some" in the following constraint: $x_i+x_j +x_k+x_l =2$ for some $i, j, k,l \in \{0,1,2,...., 10\}$, ...
M.Badaoui's user avatar
  • 185
2 votes
0 answers
125 views

OR constraint in Gurobi - Python

I'm new to Gurobi in Python and I am wondering if there is way to code the following constraints: 1- $\sum x_i =0$ for all $i\in A$ OR for all $i \in B$ where A and B are distinch sets of integers ...
M.Badaoui's user avatar
  • 185
0 votes
1 answer
133 views

How to code this constraint in CPLEX?

$$\sum_{j\in M}\sum_{k=i}^{\rm until}x_{aijk}\cdot b_{kj}=d_{ai},\quad\forall i\in N,\forall a\in B\cap A_1;{\rm until}=\min(i+v_a,n)$$ How to code this linear program in CPLEX?
Trí Vũ's user avatar
2 votes
3 answers
300 views

Create constraint only for a recourse problem in stochastic linear programming

Question1: Northam Airlines is trying to decide how to partition a new plane for its Chicago– Detroit route. The plane can seat $200$ economy class, passengers. A section can be partitioned off for ...
falamiw's user avatar
  • 157
0 votes
0 answers
63 views

Looking for correction in pyomo constraint

I am working on two graphs having nodes and edges. Graph1: VNF Graph with node demand and bandwidth demand. Graph2: Server Graph with node capacity and bandwidth capacity. The nodes and links of ...
Waqas Swati's user avatar
3 votes
1 answer
66 views

How to write a constraint to define valid agglomerations of sites?

I am currently attempting to use a MIP to optimize the agglomeration of sites to fit a minimum size. Take for example the following simplified situation of 9 sites which could be any range of sizes. ...
Musketeered's user avatar
2 votes
1 answer
122 views

Fixing a complex linear constraint in pyomo

My directed graph f with any node u has a set of outgoing and incoming links as uv ∈ O(u) and vu ∈ I(u) respectively. I am trying to write this constraint here ϕ refers to a binary decision variable ...
Waqas Swati's user avatar
5 votes
1 answer
177 views

Absolute value in an equality constraint

What is the best way to model or represent an equality constraint which includes an absolute term in the expression: $$ x = |y| $$ $x \in \mathbb{R^+}$ and $y \in \mathbb{R}$
Ahmed's user avatar
  • 103
4 votes
1 answer
177 views

Do my constraints to restrict the splitting of tasks make sense?

I have a problem where there are stations, types and tasks which has to be assigned to each other. Now for me the thing is I want the variable $x$ to be not binary like in assignment problem for ...
Harun Gül's user avatar
6 votes
1 answer
1k views

Quadratic constraints in JuMP

I am a bit new to programming and am currently working with solving optimization problems in JuMP in Julia. I got a tip from the JuMP page that I should also use ...
Annaquest's user avatar
1 vote
1 answer
51 views

Introducing WIP storage tanks in a discrete time bucket model

I have a functioning MIP model in CPLEX/OPL for production planning that generates a weekly plan of what finished good items to produce on which production resource using bill-of-materials, set of ...
S N's user avatar
  • 11
7 votes
2 answers
297 views

Set constraint mip

I am programming a MIP problem. There are two continuous variables but only one can have a value and the other must then be zero. How do I give this as a constraint?
kc27's user avatar
  • 73
5 votes
1 answer
260 views

How to solve this linear program with an exponential number of constraints?

Consider the following convex program: \begin{align*} \min g(x) && \text{such that} \\ f_i(x) &\geq b_1 && \text{ for } i \in 1,\ldots,n; \\ f_i(x)+f_j(x) &\geq b_1+b_2 &&...
Erel Segal-Halevi's user avatar
5 votes
1 answer
177 views

Should I replace equality constraints by inequality constraints if the variables in the constraint appear in the objective?

Suppose I am minimizing a MILP and my objective is simply $\sum_i{x_i}$, where $x_i$ is binary. I also have a constraint saying that $1-\sum_j y_j = x_i$, $\forall i \in \mathcal{S}$, $\forall j \in \...
cholo14's user avatar
  • 183

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