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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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Optimise number of points scored with a fixed budget

Here is my problem: I have 50 pounds to spend There are 445 players available at various prices Each player has scored a random number of points Is there a formula that will give me the the optimal combination of 11 players in terms of total…
Callum
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Is there a more efficient way to minimize this function?

I have the following function, and I need to minimize it with respect to $x$ given any constant array of positive numbers $a_0, a_1, ..., a_n$. $$\sum_{i=0}^{n}\frac{\lvert x-a_i\rvert}{a_i}$$ I recognize that this function is composed of $n + 1$…
AlphaModder
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how to get lexicographic efficient extremes by solving a scalarized (weighted sum) problem in bi-objective optimization problem?

I have a bi-objective problem: $minimize (Z_1(X) and Z_2(X))$ $Z(X)=w_1*Z_1(X)+w_2*Z_2(X)$ is the weighted sum objective function that is minimized. $Z_1(X)$ and $Z_2(X)$ are two objective functions. I want to know if there is a method or…
Masoud
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Meaning of $|\omega|=V$ when $\omega$ is a structure and $V$ is volume?

In this presentation about shape optimization by the level set method, p.2, the following definition is given: Find the most rigid structure $\omega$, of prescribed volume, contained into a given domain $\Omega$, when given external forces are…
mavavilj
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How is level set method used to find optimality?

I'm learning about the level set method in shape optimization I've only read very introductory texts on the method. However, the texts have spoken only about that the level set method (or specifically the level set function) "evolves" through…
mavavilj
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Meaning of $lw=\frac{V}{H}$ in this design optimization example?

Here, p.6, an elementary example of design (size) optimization is given. It's of a tray that has given volume $V$ and height $H$. The design problem is to select length, $l$, and width, $w$, of the tray. So, given $lwh=V$ and $h=H$, A "workable…
mavavilj
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Optimizing data usage among pooled rate plans

I'm looking for some starting tips for mathematically characterising the following problem: There are some cellular devices, each with a rate plan consisting of an amount of data and a price, like 1MB at $3/month, 5MB at $7/month, etc. Each rate…
T3db0t
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How to optimize variables within interval OR other discrete value?

The problem I have is to optimize a vector $x = [x_1, x_2, x_3, \ldots, x_n]$ where the value of $x$ can be either $0$ or within the interval of $[x_\min, 1]$ where $x_\min$ is some parameter than will be somewhere between $0$ and $1$. The objective…
Matt McConaha
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Given initial basic solution, solve using simplex method.

Consider following optimization problem Maximize$\ \ \ \ \ \ \ \ -x_1+x_2$ subjected to $\ \ \ \ \ \ \ 3x_1+4x_2=12$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x_1-x_2\leq12$ $x_1,x_2\geq0$ It is given that start with initial basic…
Abhinav Sharma
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Robust loss function for MINPACK lmdif (Levenberg marquardt)

I see that in various non-linear least squares minimization libraries a robust loss function is used to reduce the influence of outliers. See rho in here or here. This rho is applied to the squared residuals. Now, I'm using the Levenberg Marquardt…
martinako
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Find expression for $f(x)$ such that $f(x)\left(1-x - (1+\epsilon) \frac{f(x)}{1-f(x)^2}\right)$ is large

Let $x \in (0,1)$ be arbitrary and $\epsilon >0$ as small as you wish it to be. Now we want to find an expression for $0 1/c$$ for some small constant $c \in…
user136457
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Efficient ways of minimizing a complicated objective "function"?

My problem at hand neither has any special structure that gives me closed-form solutions nor can be written by a single expression. Yet, it is still an objective "function," as I can compute a value (via a chain of operations) if you give me an…
Sibbs Gambling
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Minimize the function $f(y_1,y_2)=3 y_1^2+8y_2^2$

I would like to minimize $f(y_1,y_2)=3 y_1^2+8y_2^2$ with the constraints $g(y_1,y_2)=y_1^2+y_2^2=1$. I thought I could use the Lagrange multipliers, but it is not work. Is there anyone could show me how to find it?
Sharpie
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What is the difference between these two Bellman equation?

Bellman equation: $V(x) = max \{F(x,y)+ \beta V(y)\}$ $V(x) = max \{F(x,y), \beta V(y)\}$ When to use the plus and when to use the comma? Do they get the same form of sequence problem? Would you mind give me an example to explain such…
XJ.C
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Minimum of function of $3$ variables

If $xyz = a^3$ then show that the minimum value of $x^2+y^2+z^2$ is $3a^2$. I have tried this problem using the identity $(x + y + z)^2$ but I am not satisfied with my approach. Any other method of solving it.
abhimanyu2909
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