Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [constraints]

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. Reference: Wikipedia.

There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.

984 questions
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How can I mathematiically enforce a set of constraints on a range from 0 to 1?

I have a function $f(x)$ which needs to be bounded between 2 functions $g(x)$ and $h(x)$. Functions $g(x)$ and $h(x)$ are guaranteed never to intersect. I have a function $f(x) = a + bx + cx^2$ and I need to select parameters $a$, $b$, and $c$ such…
Anon Ymous
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Pontryagin maximum principle and constraints

I have studied the Pontryagin Maximum Principle. It is about solving a problem like this: $$ \begin{cases} \min \int_{t_0}^{t_1} f(t,x,u) dt\\ x(t_0) = x_0\\ \dot x = g(t,x,u)\\ u \in U \end{cases} $$ where $U$ is the set of admissible control. We…
Nicola
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Path consistency without consistency

My math teacher has asked us to find a (not trivial) problem that is path consistent, but not consistent. I have found ones that are arc-consistent and not consistent, but I have not been able to find one that is at the same time path consistent and…
Tumata
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How to construct a set of variables that automatically satisfies certain constraints

I ran into this problem when trying to do a project on one-electron reduced matrices of fermions. The math can be formulated as following: Let $\{a_i\}_{i=1...m}$ be a set of variables with additional constraints $\sum_{i=1}^ma_i = N$, $a_i \in [0,…
L. Yu
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linear constraint on binary variable

I have to make a linear constraint for a binary variable in the following way. We have a set $S=\{0,1,\dots,k\}$ and the binary variable $b$ is defined as: $$b=\begin{cases} 1 & if\;S=1,\\ 0 & otherwise \end{cases} .$$ I couldn't…
Fabian Rocha
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restricting number of zeros in a vector

I need to make an M dimensional vector and restrict it to have R entries as zeros. Is there any expression or condition in vector form that can ensure this ?
Waqas
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Find the minimum and maximum value of a for $ 9\sum_{\mbox{cyc}} a^2 +10(ab+ ac+ad+bc+bd+cd) = 16$.

With ordered 4 real values satisfying the constraint as below, find the possible range of the largest one (i.e., the allowed interval for the variable $a$): Let $a \geq b \geq c \geq d$ be reals satisfying: $$ 9\sum_{\mbox{cyc}} a^2 +10(ab+…
Chip
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Interpretation of constraint set

Let $f : \mathbb{R}^3 \to \mathbb{R}, f(x, y, z) = x + y + z$ with constraints $$x + z = 1 \text{ and } x^2 + y^2 = 4 $$ Now it says "The constraint set is the intersection of a cylinder [I understand this, with radius $4$ and $z$ arbitrary] and a…
user1049882
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How can I formulate a linear constraint?

$C_t$ and $S_i$ are two decision variables. (1) $C_t$=$C_{(t-1)}$+$D_i$ if t=$S_i$, $\forall${i,t} (2) $C_t$=$C_{(t-1)}$, if $t\neq S_i$, $\forall${i,t} How can I present the above two conditional equations as a linear constraint? Appreciated!
SMU
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Is the following linear in the choice variables?

I have a constrained optimization problem and need to show that the constraint is concave. Similar problem usually have linear constraints, so they don't need to worry about it. However, I am not sure if my constraint is concave. I have the…
OliGopol
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How many constraints are there in $g(x) \leq 2x \geq 0$?

How many constraints are there in $g(x) \leq 2x \geq 0$? I thought $g(x) \leq 2x$ and $g(x) \geq 0$, but something suggested that there could be three rather than two constraints here? Perhaps the third one is about constraining $2x$ from…
mavavilj
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CSP arc consistency: $x > y$, $x + y < 7$

Here is the question that is my problem: Consider a CSP with variables $X$, $Y$ with domains $\{1, 2, 3, 4, 5, 6\}$ for $X$ and $\{2, 4, 6\}$ for $Y$, and constraints $X \gt Y$ and $X + Y \lt 7$. List the values that will remain in the domain…
user504783
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Prove that an empty sudoku has always a valid solution

I have to prove that if you put some random number (between 1 and 9) at any of the fields of an empty Sudoku, it is always solvable, but I do not find the way to it. One way to prove it would be solving the 9*81 possible initial values, but doesn't…
Alberto Castaño
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How can I write the following statement as a constraint?

I have the following condition: If $x = 0$ and $c=0$ then $z=1$. If $x>0$ and $c=1$ then $z = 1$. If $x>0$ and $c=0$ then $z = 0$. I find the constraint $x(1-c) \geqslant 1-z$, but it misses the last point. EDIT The variables $z$ and $c$ are…
1-approximation
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Mathematical presentation of a problem

The issue that I am dealing with now ends up with the solution of a second order equation. The solutions are the Z positions of a point in 3D. So, basically I have two points with the Z positions of $Z_i (i=1,2)$. To choose between these two points…
NESHOM
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