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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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Smallest distance to box

This is probably an easy question, but I am not capable of solving it. I have two particles which distance of each other is $r$. One particle is inside a box with diameter $d$. Now I want to determine the smallest distance from particle 1 to the…
Gilfoyle
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Minimizing a variable by maximizing two functions

I have below objective function: $$ \min_{x\geq 0} (\max \{ x, 1/x \} )$$ where, $x \geq 0$. Can anyone please tell me how to proceed for this? Matlab says minimum value for $x$ is $0.1$, since I set boundary to .1, but thats not intuitive.
jhon_wick
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optimization of min/max from point C and circle C to a line

this is the question, am i allowed to post the question? basically i know all the formulas and how to sub to get a distance between two points, but i just cant find out how to do this... Im supposed to present it such that its min d, being the…
Althea C
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help me minimize this sum

I want minimize $\sum_{i} ^{n} w_i^2$ such that $\sum_i ^{n} w_i=1$, and $w_i>0$ simply taking the derivative and set it to zero won't work. The answer is probably $w_i=1/n$, for all $i$. But I don't know how to show that. Any thought on this?
wrek
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When can we say that a portfolio is optimal

I've been interested in portfolio optimization for a while now and I kind of read articles about it all over the web trying to go from the beginning (Markowitz - Merton ...), there's one thing I still can't really understand. Here is how I see the…
mlx
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Simple Optimization problem

somehow I'm not able to solve this: $f:\mathbb R^2 \to \mathbb R, \quad (x,y)\mapsto 2x^3-12x+3y^2+6xy$ $D:=\{(x,y)\in\mathbb R^2 | x\geq 0, y\geq 0 , x+y\leq 1\}$ Get the extrema on $f|_D$ Solution: Define $g(x,y):=x+y-1=0$ Define $L=f-\lambda…
xotix
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A high school optimization problem

$x$,$y$ and $z$ are real numbers. We have two equations which are given by the following: $x+y+z=5$ $xy+yz+zx=3$ By using the two equations above, find the maximum value of $z$. How can we solve that question by using derivatives or without using…
ötarcan
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An optimization problem with positive real numbers

$x$ and $y$ are positive real numbers. How can we find the minimum value of the sum $(16/x)+(108/y)+(xy)$ ? It seems to be a easy question but I could not even decide where to start...
ötarcan
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Calculating work duration based on man-months and efficiency percentage

I am attempting to confirm some calculations given to me during class, regarding the work duration of different projects. This table concerns a 100 man-month project, where using the Optimal Span Hypothesis the the efficiency percentage is…
two_Thomas
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Can I say the following statement?

Can I say that "If a problem is formulated as a linear problem (LP), then there must be a solution to the problem (theoretically)"?
Dave
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Are hyperplanes linear?

I have a question as to what someone means when they speak about hyperplanes. In "A combinatorial bound for linear programming and related problems", they mention hyperplanes without really defining them, and I would really like to know what they…
user1582024
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Proof of Güler Lemma 1.17, a multivariate Mean Value Theorem alternative

I started reading Güler's Foundations of Optimization today, and I'm having trouble with the proof of Lemma 1.17. I've already found errors in the book, so I'm particularly suspicious at this point. Lemma 1.17. Let $f : I \to \mathbb{R}^m$ be a map…
user144527
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How to solve an optimization problem with max in objective function

For example. The problem I'm working on is \begin{align} U(x,y)=(\max\{x,y\}+2)^3+5 \end{align} I had a problem where min was in the objective function before, so I would set $x$ and $y$ equal. I'm sure that's not the same in this situation but…
Shaner
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How can I find absolute max and min points in a circle?

I have $f(x,y)=x^2-y^2$ and need to find absolute values in the region defined by $x^2+y^2 \le 1$ I have a solution that my teacher gave me, where $r(t)= (\cos t, \sin t)$ with $0 \le t \le 2\pi$ $$f (r (t))= g (t)=\cos^2 (t)-\sin^2 (t)$$ And its…
Floella
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Question on Danzig selector

Let $A \in \mathbb{C}^{m \times N}$ be such that, for some constants $0 , \rho < 1$ and $\tau \geq 0,$ $$\| v_{S} \|_{2} \leq \frac{\rho}{\sqrt{s}} \| v_{\overline{S}}\|_{1} + \tau \|A^{*}A \|_{\infty}~\textrm{for all}~S \subset [N]~\textrm{and…
Rajitha Ranasinghe
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