# Questions tagged [constraints]

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

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### How do I determine the maximum subgraph that avoids certain edges?

I have a graph where I want to select a subset of the nodes subject to a particular constraint: An edge between nodes A and B indicates that I cannot select BOTH A and B to belong to the subset. I ...
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### Proof of solvable constrained optimization with a subset of a larger set of constraints

Way out of my comfort zone here so apologies if I'm not providing enough or correct information. I work with an application of constrained optimization to assemble test forms (automated test assembly)....
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### Deriving correct integral constraint equation for calculus of variations problem

I have the following calculus of variations problem: $$\mathcal{L}=-2X'(t)\ln{x'(t)}-2Y'(t)\ln{y'(t)}$$ where $x(t)$ and $y(t)$ are the functions I'm interested in, and $X(t)$ and $Y(t)$ are given as ...
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### How to add discrete function constraints to a calculus of variations problem

Suppose that $L$ is the Lagrangian of a system and $f$ is a function of $x$. The objective is to find a function $f$ that optimises: $J[f] = \int{L(x, f, f')}dx$ How do you fix the value of $f(x)$ at ...
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I'm trying to explain how to use Lagrangian multipliers, through an example. I start in this way: Understanding how Lagrangian multipliers work can be done through a simple example. Consider the ...
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### Can we assume for free the upper bound for a variable in the minimization problem $\min_{(x,t) \in \mathbb{R}^n\times \mathbb{R}} t$?

Problem: Let us consider the following minimization problem \begin{align*} &\min_{(x,t) \in \mathbb{R}^n\times \mathbb{R}} t\\ \text{s.t }& \Vert x-q_i\Vert^2 \le r_i^2 + t,\ \forall i = \...
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### Optimization constraint

I'm learning optimization and I came across equality constraints. Lets say we have an objective function J defined over $V$ with values in $\mathbb{R}$, where $V$ is the normed vector space in which ...
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### Optimisation Problem Setup and KKT conditions

I am trying to setup an optimization problem with equality and inequality constraints. I want to estimate a specific variable call $\chi$ subject to a minimisation problem -- guidance on the setup and ...
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### Point isolation through linear constraints

I consider a set of $n$ points in $\mathbb R^d$: $X=${$x_i$}$_{i=1}^n$. I would like to know for each point $\tilde x\in X$ if there exists a dimension $j\in${$1, ..., d$} and $k$ linear constraints (...
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### Discrete point inside a polygon formed by set of vertices

I am working on a problem where I have a set of 2D vertices and a test point. I want to check whether the test point lies inside the polygon formed by the set of given vertices. I am trying to model ...
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### Same sign constraint in linear optimization problem

I'm trying to find a way to force a group of variables to take the same sign. Either positive or negative. Clearly, the fact that an OR statement is required implies that the problem becomes non-...
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