Mathematics Stack Exchange
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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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How to solve word problems about polynomials given a rectangle and the following I have tried all i know?

The question is Mr.Bryant wants to add a new rectangular screened porch onto his house.The cost of the screen porch is the function of its size. The length of the porch must be twice its width the materials cost approximately 55 dollars per square…
MATH ASKER
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Existence of solution to maximization problem

I'm a first year Finance grad student and we're learning utility maximization problem now. We have been assuming that a solution to these problems exists. Are there any general theorem about the existence of maximization solution on $\mathbb{R}^n$?…
Kenneth Chen
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Relaxed quadratic pseudo-boolean optimization

Quadratic Pseudo-Boolean Optimization (QPBO) problem: Problem 1. Minimize $\sum_i a_ix_i + \sum_{i
f10w
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Maxima and minima of $x\sqrt{3-x^2}$

Regarding the function $f(x) = x\sqrt{3-x^2}$, I can determine that there are local min/max at +/-$\sqrt{\frac{3}{2}}$. I assumed these would also be the global max and min after looking at the graphed function. However, when I try to confirm my…
user184881
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Improving Newton Iteration

I am a problem a to determine a minimum of a function by a method using the iterative gradient methods and Newton. Whether à function of type $f(x,y)=100\cdot(y-x^{2})^{2} + (1-x)^{2}$ how I can to determine with the methods of gradient and newton…
Paul-henri Guet
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Is a hyperplane also a halfspace?

In general polyhedron(as a feasible region of a lpp) is nothing but intersection of finite number of half spaces. Now polyhedron in standard form is represented by intersection of hyperplanes(Ax=b) and halfspaces(x>=0). So, it should also match the…
Ani
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Minimizing a function

For any $\rho$ we want to minimize this function. The minimum of $\pi$ is obtained at a point where $x_2 = \frac{1}{2}x_{1}$ and where $x_1$ minimizes the function defined by $$\begin{cases} \frac{1}{4}x_{1}^{2}-\rho(x_{1}-1),& \text{if} \ x_1 <1…
Shawn
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Finding the maximum value of a fuction in two variables

I know how to find the absolute maximum and minimum values of a function in one variable. It can be found by differentiating the function and sitting it to zero and then solving for the unknown. But i would like to know how to find the maximum value…
user258250
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Wanted: Examples of how black box optimizer works - step by step?

I need to understend how black box optimizer work. I need a real life example of how it hlps. So what I need: What was the task, what were parameters, what was the function to minimize and how it all worked toogether. I need deteiled info on this…
Kabumbus
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Algorithm for maximizing the overlap between sets of voxel points

I have a problem that I've formulated as follows. Given a finite target set $T$, and a set-generating function $F(x_i) = C_i$ that also produces finite sets, I'd like to find the set $C_i$ that has maximum overlap with $T$. As far as I've been able…
voxelite
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Need help figuring out routing problem

Thanks in advance for helping me with this routing problem. It's for a digital instrument I'm building, six sine-wave oscillators that feed back into each other in a kind of recursive web. Here's the mission: You have six modules. Each module…
rachMiel
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Showing a $\mathbb{R}^3 \rightarrow \mathbb{R}$ function attains a global minimum at the origin without using calculus.

Given $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ defined as $$f(x) = x^2 + 3y^2 +2z^2 - 2xy + 2xz$$ I am trying to show $f$ attains a global minimum at the origin without using calculus. I was thinking of completing the square for a start, but I am…
Linda
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How to solve a Robust Linear Program problem?

How to solve a Robust problem? For example if I have the following Robust LP. minimize $\beta$ subject to $3x_1+4x_2 \leq7$ $3x_1 \leq7$ $x_1 \geq 0$ $x_2 \geq 0$ $-x_1+4x_2\leq\beta$ $x_1+4x_2\leq\beta$ How should I tackle this problem?
Steven
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Maximum likelihood of fraction

To maximize the log likelihood of my parameters, I need to find the argument that maximizes the following function: $$\sum_{\substack{i,\,j\\ i \neq j}} n_i \log(x_i) + n_j \log(x_j) - (n_i + n_j) \log(x_i+x_j) $$ The $n_i$ have a known value, the…
DevShark
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optimization of normalized quadratic function

I'm a computer science student. Please I need a help in solving a constrained normalized quadratic function. I'm familiar with solving quadratic constrained optimization function with matlab by providing a symmetric matrix and a vector as inputs for…
MahopeRam
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