Mathematics Stack Exchange
Mathematics Stack Exchange

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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Is it possible to calculate the following optimization expression?

I'm faced with this expression: $$max(xy) : x \leq a, \; y \leq b,\; c = \frac{x}{y}$$ where all variables are greater than or equal to zero. I know the values for a, b, and c but I need to find the maximum value for x * y and the values for x * y…
rtheunissen
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Minimum number of emails to be sent

There are n colleagues and each has a unique document.These documents need to be shared through emails. An email can be sent only to one person at a time (so no cc/bcc is allowed) although an email can have multiple documents attached. What is the…
Amit Trivedi
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Duality for Support Vector Machines

SVM classifier for two linearly separable classes is based on the following convex optimization problem: \begin{equation*} \frac{1}{2}\sum_{k=1}^{n}w_k^2 \rightarrow \min \end{equation*} \begin{equation*} \sum_{k=1}^{n}w_k x_{ik} + b \geq 1,\;…
Leo
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Symbolic evaluation of an optimization problem

I'm looking at the following problem: Minimize $\sum_{i=1}^{m} \frac{x_i}{x_{i-1}}$ under the constraints $-x_0 \le -1$, $x_{i-1} - x_i \le 0$, and $x_m \ge N$ where $N>0$ and $m>0$ are some constants. What methods can I use to evaluate this…
somebody
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Minimum time for parallel execution

Suppose to have 2 worker and they must do a task multiple times. Worker A and Worker B have a different work speed. How can I calculate the minimum time for doing the task N times? For example: I need to do the task 15 times. Worker A finish a…
Emanuele
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Finding a stud (i.e., in a stud wall:)

During a thread in a private usenet newsgroup, involving finding a stud in a stud wall, somebody posted what I believe is the typical procedure (when the typical hardware store studfinder doesn't work)... Scott D wrote: ...take a a very thin…
John Forkosh
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Maximize $x_1$ and $x_2$

I have the following question to tackle: Maximize $x_1$ and $x_2$ for: $$ x_1, x_2 \geq 0$$ $$ -x_1 + x_2 \leq 5$$ $$ x_1 + 4x_2 \leq 45$$ $$ 2x_1 + x_2 \leq 27$$ $$3x_1 - 4x_2 \leq 24$$ So I just wrote out these constraints as the following…
Ylyk Coitus
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Linear Programming Duality

Consider an LP problem in standard form and its dual. If the dual problem has a non-degenerate optimal solution, then the primal problem has a unique optimal solution. I know it is true, but how should proof it.
Kath
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Minimizing average distance to closest points

I have a problem that I'm not sure how to solve. Here's the problem. Suppose I have a one-dimensional space with people distributed some way over that space. They could be normally distributed, they could be uniformly distributed, they could be…
Adam
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Obtain the maximum and minimium of the function $f$

I have to calculate the max and min of the function \begin{equation} f(x_1,x_2 \ldots ,x_n)=x_1^3 + x_2^3+\cdots + x_n^3 \end{equation} subject to \begin{equation} x_1 + x_2+\cdots + x_n =0 \end{equation} \begin{equation} x_1^2 + x_2^2+\cdots +…
galba
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How to get from high school math to optimization?

What are the math subjects that a person with high-school math background needs to learn to reach the point of learning and understanding different techniques of mathematical optimization? It would be helpful if the subjects are listed in the order…
Ashwin Nanjappa
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Optimal cuts from pipe

I need to make a program that calculates the optimal way to cut pieces of pipe to what a customer wants. My advanced math skills are bad but I know this is the cutting stock problem. My first problem is that I don't really understand much on that…
Mike
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Textbook Exercise on Linearly Constrained Optimization

I'm having a bit of trouble with the following exercise: Let $f\colon \mathbb{R}^n\to \mathbb{R}$ be given by $f(x)=\|x\|$. Consider the problem of minimizing $f$ subject to $Ax=b$, where $A\in\mathbb{R}^{m\times n}$, $b\in\mathbb{R}^m$, $m
Ariel Serranoni
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An optimization problem

I need to prove the following result: Given a real sequence $a=(a_n)_{n\in\mathbb{Z}}$ and a number $A>0$ then $||a||_{1}\leq A$ if and only if there exists $b_n$ such that $-b_n\leq a_n\leq b_n$ holds for any n and $\sum\limits_{n}b_n\leq A$,…
Tao
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Does a collection of non-linear inequalities have "extreme points"

Say I have a collection of m non-linear inequalities, where each of the $i = 1... m$ inequalities has the form: $g_i(x) \leq 0$ where $g_i: \mathbb{R}^n \rightarrow \mathbb{R}$ and $g_i(x)$ is nonlinear with respect to $x \in \mathbb{R}^n$ Let…
Elements
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