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
-1
votes
1 answer

How to use CVX to deal with the constraint $X^T X - Y^T Y \geq 0$?

Let $X, Y \in \mathbb{R}^{n\times n}$. How to deal with the constraint $X^T X - Y^T Y \geq 0$ in CVX? Thanks very much!
Ryan
  • 655
-1
votes
1 answer

Optimization problem for $n$ components with sum being $1$

I have this problem, could you guys help me? And how can I code this in Python? Thank you so much! Calculate max value of: $x_1x_2 + x_1x_3 + ... + x_{n-1}x_n = \displaystyle \sum_{1 \le i < j \le n}x_ix_j$, given that $x_1 + x_2 + ... + x_n = 1$.
anhdroid
  • 13
-1
votes
1 answer

Proximal Operator

I am having trouble to calculate the proximal operator of $f(X)=\|X-Q\|_{2}$, where $Q \in \mathbb{R}^{n}$. I will really appreciate any kind of suggestions. My approach, \begin{equation*} \begin{split} \operatorname{prox}_{\lambda…
Robin
  • 1
-1
votes
1 answer

Find Minimum of Variance

Given the Variance $\sum_{n=1}^{\infty}\frac{c\Delta\mu_n-\Delta(\sigma_{n}^{²}+\mu_{n}^2)}{P_{n}}$ and $ \sum_{n=1}^{\infty}P_{n} = \mu$. I would like to minimize Var by choosing the best $P_{n}$. Can somebody give me a hint how to get to the…
Jordan
  • 3
-1
votes
1 answer

Reduction of a whole to parts

I am looking for a way to produce a given total ($n$) using fixed parts $(a, b, c)$ in multiples $(x, y, z)$: $ax+by+cz=n$, in such a way that $x+y+z$ is as small as possible, using integers only. An example: where $n=50$, $a=9$, $b=7$, and $c=4$,…
RS Piper
  • 1
-1
votes
1 answer

Is there an ideal scoring term for determining two numbers?

Let's say I have a known vector of two numbers: c(A,B) Is there a scoring term, or a combination of scoring terms, that can measure the unique closeness of a random vector c(a,b) to the known vector? In other words, is there a scoring term that can…
Nova
  • 660
-1
votes
3 answers

Extremizing product over the standard simplex

I just stumbled across the following optimization problem with boundary conditions: $$\begin{array}{ll} \text{extremize} & \prod_i x_i\\ \text{subject to} & \sum_i x_i = 1\\ & x_i > 0\end{array}$$ How can I approach this problem?
Gilfoyle
  • 401
-1
votes
1 answer

Maxima for max output

How can i find a maxpoint of equation For example : y=3.2155x+35.85 now i want two x: x1+x2 at which y1+y2 is max. where x1+x2=30 I want to find values of x1 and x2.
Noman jabbar
  • 3
-1
votes
2 answers

Optimization of rectangle. Find size of fence

I've got this, and im unsure how to proceed. I need to build a fence. There is a building next to the fence, which is why i only need $3$ sides of the fence and it shall be a rectangle. So this applies: $o=2x+y$ The area shall be $558m^2$ So…
Exobit
  • 1
-1
votes
3 answers

Minimum of $f(x) := x^2$ subject to $g(x) := 2 x + 1 = 0$

If I want to find the minimum of $f(x) = x^2$ subject to the constraint $g(x) = 2x + 1 = 0$, then I would first isolate $x$ from $g$ and insert into $f$: $$ 2x + 1 = 0\\ x = -1/2 $$ So $$ f(x) = x^2 = (-1/2)^2 = 1/4 $$ And now set the first…
TMOTTM
  • 177
-1
votes
1 answer

probability consumer will

So I've been reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated with Field Experiments" by Fisher, Gallino, and Li. Within the paper they provide a formula that calculates the probability Prjr that a consumer…
amadzebra
  • 1
-1
votes
1 answer

optimization model & method

I have question about optimize problem need to proof: suppose that $M$ is a symmetric matrix, then the following are equivalent: (1) $||M^{-1}|| < \frac{1}{h}$, where $h > 0$ (2) $||Mv|| \geq h||v||$, where $h>0$, $v \in \mathbb{R}^n$ proof from (1)…
john
  • 1
-1
votes
2 answers

What does the hessian matrix tell me when optimizing a problem

I'm wondering what the hessian matrix of a function tells me about its critical points. Quick Example: Let $f(x,y) = \frac{x^2}{2}+\frac{y^2}{2}$ and $M:=\{(x,y)\in\mathbb R^2 | \frac{x^2}{2}+y^2\leq1\}$ We get a minima in $p_1=(0,0)$ and two maxima…
xotix
  • 887
-1
votes
1 answer

Minimisation problem of two equations with three variables

I have 2 equations with 3 variables. I need to find the minimum points for the 3 variables. The question as below: Equation 1: $$ 0.09518x - 0.06118y - 0.06132z = 4.031 $$ Equation 2: $$ 0.0049x=0.1738 $$ where constraint of $x,y,z$ is $30$ and…
KCL
  • 1
-1
votes
1 answer

Jacobian of minimization function

I'm currently trying to compute an exact jacobian for scipy's optimize.minimize function. For the fitting routine, it's a mixture of Gaussian peaks, and I am optimizing the number of Gaussians as well as the peak parameters. For my error function, I…
Chrismit
  • 99
1 2 3
…
97
98