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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").

22512 questions
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Proof that null is a minimum

I was corrected that the following calculation is not correct, maybe you can help me finding the mistake: The mathematical (well known) task was: A person on a lake (distance to coast: d) wants to reach a point P on the coast (the coast has a…
Vazrael
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How can I find solutions of a multivariable inequality?

Let's suppose I have an inequality like $ax+by+cz<30$ with $1
Xristos Lymperopoulos
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Find a minimum of a function with constraints (separating hyperplanes)

I'm reading "The Elements of Statistical Learning", to be precise chapter about optimal separating hyperplanes (SVM classification problem) and I've stuck with the following. I have a function to be maximized: $$ \sum_{i=1}^{N}a_i -…
Anthony
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solution to knapsack like problem.

I am new to optimization. How do I solve the below problem? Is it similar to the 0-1 knapsack problem? There will be a meeting at New York and San Francisco offices. We will have to fly the participants to either one of these two offices. Let's say…
mathopt
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How can two runners be faster than one? An optimization puzzle.

Puzzle Two identical runners are supposed to transport a message from A to B across a distance $d$ in minimal time $t_{min}$. Preliminaries The capacity of the two runners is described by their maximal speed $v_{max}$ a function $T(d)$ giving the…
Hans-Peter Stricker
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Existence of minimizer of a special functional

Let $U$ be an open subset of $\mathbb{R}^n$ Consider the minimization problem for \begin{equation} I[w]:=\int_UL(Dw(x),w(x),x)dx \end{equation} where $w:U\rightarrow \mathbb{R}^m$, $L:\mathbb{M}^{m\times n}\times\mathbb{R}^m\times…
CSH
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Show that exactly one of the equations has a solution.

Show that exactly one of: \begin{cases} B^Tv = 0\\ d^Tv = 1 \end{cases} or $$Bu=d$$ has a solution. I tried with Farkas lemma, but I run into trouble.
Johan
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Reverse a simple equation of value to scale

I'm trying reverse the following equation, consider this: i've done this to get a value to scale from Max to Min, example i put a x value bigger then i get a small value, so i've tried reverse and i've done something like this: but i have not got…
MindLerp
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Are the extrema of a product of smooth positive functions the same as those of a sum of the same functions?

Given a couple of strictly positive functions, is optimizing the product of these functions equivalent to optimizing their sum? Any proof or counter example in the literature?
Mpampa
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maximization or minimiation linear optimization

I'm just studying for a maths exam I have in a few weeks and the notes my teacher gave me contradict so much on the internet that now I'm really confused. In his notes he says the standard form of an LPP is a minimization problem and we should…
richard davies
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Minimise $\|h-h_i\|+\lambda\|h-u\|$ for $\lambda \in [0,100]$

I would be thankful if anyone can answer my question. This is a very basic question. Let's say we wish to minimise the quantity $$\hat{h}= \|h-h_i\|+\lambda\|h-u\|,$$ where: $$h=[13,17,20, 17, 20, 14, 17, 18, 16, 15, 15, 12, 19, 13, 17,…
Muhammad Imran
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Optimizing a formula with a large number of potential choices

I have 800 names, each with a unique cost and value. I need to pick 20 individuals out of the 800, with a total cost of under $60. Is there a program I can use to optimize a formula to find the best combination of choices? I'm not familiar with much…
Gavin Bock
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optimization related to cdf

When $\psi(\lambda) = \int_{-\infty}^{\infty}\{\Phi(\lambda x)\}^{K}\phi(x)dx$ is maximized or minimized with respect to $\lambda$? Where $\Phi()$ and $\phi()$ are usual distribution function and density function of standard normal distribution.
Satya Prakash
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Maximizing a non-concave objective

I want to maximize this function $\log_2(1+p)+e^{-p} $. The second derivative is $-\frac{1}{\ln2 (1+p)^2}+e^{-p}$ Is there any way to get a unique solution for p ?
user7341333
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Finding optimal blend of items to meet certain criteria

Math beginner here. Say I have the following items Marsbar: sugar 100/lb, salt 5/lb, price $4/lb, inventory: 40lb Twix: sugar 100/lb, salt 9/lb, price $7/lb, inventory: 9lb Bounty: sugar 105/lb, salt 4/lb, price $3/lb, inventory: 10lb and I…
acrmuui
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