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.
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Show that $\min\{a_1,a_2,…,a_n\}$ is maximum when $a_1=a_2=…=a_n$.
Given $a_1,a_2,...,a_n\in\mathbb R$, and $a_1+a_2+...+a_n=A$. Show that $\min\{a_1,a_2,...,a_n\}$ is maximum when $a_1=a_2=...=a_n$.
I feel this is quite a common sense but I don't know how to ...
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3answers
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Underdetermined System and Minimizing Cost
I need to minimize 4x + 4y subject to the following constraints:
$4x + 8y = 40$
$x + 2y = 10$
Any ideas? Answers must be integers, as they represent physical units.
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Nonlinear optimization of constraint parameter - subdifferential?
Disclaimer: I discovered that the FAQ suggests to post research-level to mathoverflow instead of math.stackexchange. I "moved" the question accordingly, cp. post at mathoverflow. Sorry for the ...
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Optimize winnings in a money making game.
So, given a continuous random variable A (with some density and CDF function), and a value I choose V, what is the equation to determine the best value V to maximize my earnings given that I will be ...
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calc word optimization problem
a power line runs north-south. Town A is 3 miles due east from a point a on the power line, and town B is 5 miles due west from a point b on the power line that is 9 miles north of a. A transformer, ...
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Questions about the Bresenham Line Algorithim?
For my AP Computer Science class we had to write a code illustrating the effectiveness of Bresenham Algorithm, an optimization type problem.
I have some questions about the algorithm.
Let us say ...
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2answers
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Maximum of $3x^2e^{-x^3}$
I have a PDF which looks like:
$f(x) = 3x^2e^{-x^3}, \quad x \geq 0 $
I need to find it's maximum (to sample from it using the rejection method), so I differentiate and set the result to $0$:
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Linear Program Transformations
I have a Linear Program with constrains of the form:
$$a_{11}x_1+a_{12}x_2+\ldots\le 0$$
$$a_{21}x_1+a_{22}x_2+\ldots\le 0$$
$$a_{31}x_1+a_{32}x_2+\ldots\le 0$$
My problem is that if I try to ...
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1answer
55 views
Question on the perimeter of any quadrilateral
Is it true that the perimeter of any convex quadrilateral inside a unit circle
is no more than $4\sqrt{2}$?
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2answers
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Analytical Solution to a simple l1 norm problem
Can we solve this simple optimization problem analytically?
$ \min_{w}\dfrac{1}{2}\left(w-c\right)^{2}+\lambda\left|w\right| $
where c is a scalar and w is the scalar optimization variable.
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Optimization with non continuous derivative
I want to minimize the following function
$$f(x) = \max_k (\ g_k(x)\ )$$
I intend to compute the minimum by means of numerical methods, such as the Newton-Raphson method.
Newton-Raphson requires ...
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What's the solution to this optimal control problem?
I have the following control problem:
Objective: to find $p_t$ that
$$
\max_{p_t} \sum_t^T \left(c p_t u_t - k (1-p_t)^2 \right) e^{-\beta t} \tag{1}
$$
Constraints (for all $t$):
$$0 \leq p_t\leq 1 ...
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2answers
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How to find the minimum value of the expression?
Let $x$, $y$, $z$ be three nonegative real numbers and $x^2 + y^2 + z^2 = 5.$ Find the minimum of the expression
$$E=\dfrac{1}{2}(x^2 y^2 + y^2 z^2 + z^2 x^2) + \dfrac{96}{x + y + z + 1}.$$
What ...
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Linear programming vs. Integer programming
I was trying to solve a problem where I want to choose which items to choose where each item has a number b_i associated with it and a reward r_i associated with it. I need to choose items that ...
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0answers
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Issues with solving large sparse linear equations
I have some issues solving sparse linear equations Ax = b
My matrix A is sparse with dimension of 5 million by 5 million. Actually, it is a combination of two matrices. One is tridiagonal and the ...
