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").

22512 questions
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Is this function convex?

I have a model - function of two vectors $A$ and $B$. I have data that I want to fit to the model and find the model's parameters. The function needs to be convex to find the parameters using optimization; my question is: is the function convex? The…
Jakub M.
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Is there a mathematical approach to optimizing given these conditions?

The idea is you have a set of things that you know and a problem to solve. Sometimes you think you know enough but are wrong. Sometimes you think you don't know enough but are wrong. In one case you should have taken the time to learn more. In…
Aaron Anodide
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Compute the generalization of average

Consider $n$ real numbers $a_1, \ldots, a_n$. Let $x_p = argmin_{x} \sum_{i=1}^n |a_i-x|^p$. I know $x_2$ is the average. $n$ is odd, $x_1$ is the median. How about other $p$'s. Are there simple analytic forms or one has to use optimization…
Chao Xu
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Finding a local minimiser

I have a function $$f(x)=3e^{2x} -10x -7x^2$$ Using the grid search method with three internal points and using [0,1] as the starting interval, I get the solution 1.3964 after 4 iterations. Could anyone verify this please?
user204450
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Optimization of shapes

I'm in grade 9 and very soon, I'm going to have my final exam in math. Now, I'm pretty decent with almost everything I learned in math, except the optimization of shapes (especially rectangles.) My question is: How do you optimize rectangles, so…
Braydon.E
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Finding the Point at Which a Function is a Maximum when the Derivative is a Transcendental Function

Take $$ f\left(x\right)=-x\left( x\sqrt{4-x^2}-4\arccos\left(\frac{x}{2}\right) \right)\arccos\left(\frac{x^2+d^2-1}{2dx}\right) $$ and try to find the point where $f$ is at a maximum, given $1< x<2$. I've tried solving $f'\left( x \right)=0$ but…
apg
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Minimizing a function with absolute value in one variable

Minimize the following scalar function: $f(x)={\frac 1 2}(x-b)^2+\lambda|x|$ where $b$ and $\lambda \ge 0$ are given real parameters. I need to show that the function is convex and find the unique minimizer $x^* = x^*(b; \lambda)$. I figured the…
Bryan Walker
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Assigning people to events & events to time and place

I'm helping organizing a one-day conference which will host 6 events and a few hundred people, and wouldn't mind some help myself. There are four locations we've staked out with varying capacities, and three time slots of equal length. Each event…
concat
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Modified bin packing problem

What is known: There are $b_i$ boxes of type $i$, where $i=1, \ldots, n$. There are $3$ types of truck, each can carry at most $K_1$, $K_2$, and $K_3$ boxes respectively. Each type of truck has unlimited supply. The costs of using each type of…
hans-t
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Relationship between maximum and minimum of a function

Does $\max(f) = -\min(-f)$ hold generally?
nomadStack
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Maximize $\text{trace}(Z^{T}A Z)/\text{trace}(Z^{T}B Z)$

I am trying to find $Z$ in the following problem: \begin{equation} \begin{array}{c} maximize \hspace{2mm} \frac{\text{trace}(Z^{T}Lb\hspace{2mm} Z)}{\text{trace}(Z^{T}Lw\hspace{2mm} Z)}, \\ \end{array} \end{equation} for $Z \in…
user205035
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Counting the number of solutions to an equation.

In my work I am dealing with an equation that will have 1 or more solutions. Specifically I am trying to find local maximums. I am not interested in the solutions to the equation, but I am instead interested in how many solutions there are. Is there…
mjnichol
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Maximizing the sum of nonnegative functions.

I was trying to solve the problem A maximization problem when I ask myself if the general problem \begin{equation} \begin{array}{c} maximize\hspace{1cm} f(\mathbf{X})^p +g(\mathbf{X})^p \\ s.t. \hspace{1cm} \mathbf{X} \in K \subseteq \mathbb{R}^{m…
Alex Silva
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Optimization problem with integral

I have here quite a easy optimization problem, however I can't figure out how to solve it. Given a definite integral from a to b. I need to find values a and b such that the value of the integral is largest. How do I solve su
Schidu Luca
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Does the terms 'LP primal' and 'LP dual' usually refer to any primal/dual, or just the optimal primal/dual pair

As the title says, I'm wondering whether the terms LP primal and LP dual usually refers to any primal/dual pair of an LP (feasible or not), or just the optimal primal/dual pair. The reason that I'm asking is that I found the following question…
riklund
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