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Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

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Optimization with vectors

I don't know if there exist a simple solution. But I have the following problem: I have a vector positive $m \in (\mathbb{R}^{+})^n$ and a set of vectors (which can have negative composants) $(v_1, v_2, \cdots, v_M)$ each of this vectors are in…
sailx
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Find the nearest fitting image

Say that I need to resize an image into 104cm x 232cm (width x height). I have various different folders to pick an image from to resize, while each folder is of different sizes. "80x200", "90x200", "90x205", "90x210", "90x230", "100x200",…
avizzzy
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Max possible area of a rectangle that has its corners on the inverted parabola

I have to find the max area of a rectangle in an inverted parabola with the equation y=3x(4-x). I expanded the equation to be 3x^2-12x+h to find where the corners lie on the x-axis. If i solve for h, will that give me my 2 corners that lie on the…
Michael
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Find dual from primal optimization problem

I need to find the dual to the following optimization problem: $\text{max} \{c x: A x \leq b, C y \geq d, x+y \geq 0\}$, where $A$ and $C$ are matrices and $c$, $b$, $x$ and $y$ are vectors. In order to so, I want to find a matrix $A'$ and a vector…
Robin Egberts
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Positive Square Exercises

I'm trying to do these problems, but I'm not sure how to start. Can someone help me figure out how I'm supposed to approach these? Thank you Let a, b, c be positive constants. For all positive numbers x, y with product c, find the minimum value of…
user593248
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Which catalog does an optimization problem with decision variables in indicator functions belongs to?

Which catalog does an optimization problem with decision variables in indicator functions as following belongs to and how to solve it? $$ \begin{align*} &\min_{\mathbf{d}, \mathbf{m} \in \mathbf{R}^{n}}\quad z=\sum_{i=1}^{n}…
XWei
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Extrema of $f(x):=e^{x(y+1)}$ on $\mathcal C_1^{\|\cdot\|_\infty}$

$$f(x):=e^{x(y+1)}$$ Are the extrema on $\mathcal C_1^{\|\cdot\|_\infty}$ where $\mathcal C_1^{\|\cdot\|_\infty}$ denotes the closed circle around $(0,0)$ with radius $1$ (sup norm!) the same as on $\mathcal C_1^{\|\cdot\|_2}$? $\mathcal…
user586087
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Simple but not simple Nonconvex Optimization Problem

everyone. Just bump into one nonconvex optimization problem. Looks simple, but I dont know how to solve it. The problem is $\max_{a,b,\tau} \tau$ $\text{s.t.} \tau\leq \tau_{1}(a,b),$ $\tau\leq \tau_{2}(a,b),$ $a_{\text{min}}\leq a \leq…
Holt Zerng
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The sum of two nonnegative numbers is 36. Find the numbers if A) the difference of their square roots is to be as large as possible.

The sum of two nonnegative numbers is 36. Find the numbers if the difference of their square roots is a maximum. $x + y = 36$ and $S = \sqrt{x} - \sqrt{y}$ I keep coming up with X = 18 which gives me 0 in the 2nd derivative test but it is not a…
kam
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Optimization using Hungarian Algorithm

I have a problem where I have to pair workers to perform task. This means that each pair p-q can only perform a task t. I have to optimally find for each task t, which pair can best perform the task optimally for assignment. How can I convert this…
leutsoa moteka
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Find the quickest path through a mixed-density fluid

Sort of like a more advanced version of this question. Given a continuous 2D or higher function $f(x, y)$ corresponding to speed of getting through that point and two points $\vec{a}, \vec{b}$ to travel between, find the quickest route through. For…
Lightning Creations
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minima of a multivariate function

Say I have a function of 2 or more variables f(x,y,...). There is nothing given about the function (concave, convex etc). Is it always the case that minima you get by forcing some of these variables to zero always greater than what you get…
dayum
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Constrained optimization set up with at least one value constraint

I am working through setting up a optimization problem as: min Ax s.t. x ≥ 0 Where A is of size 1xp and hence x has size px1. How do I add a condition such that at least one of x has value 100.
user1243255
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Two-dimensional optimization: need an appropriate measure of confidence

I have a fitness function $f(x,y)$, which I am sampling at discrete $x$ and $y$ in order to minimize $f$. In addition to the location of the minimum, I would like to give an appropriate measure of confidence or quality of the determined location,…
Hendrik
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Geometric and arithmetic mean

The positive integers $a
SuperMage1
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