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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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Help with what optimisation technique to use

For this equation, I was wondering if I could get some help on how to optimise this (minimising surface area with volume as a constraint) Equation to be optimised (I was trying to take a partial derivative for one of the…
Ray Yao
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Optimisation of an ellipsoid

I was wondering is it possible to try and do optimisation of an ellipsoid given the formulae for its volume and surface area? I would be trying to keep the volume constant whilst minimising SA. This is for one of my maths investigations, basically…
Ray Yao
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Constrained optimization problem with multiple variables

I need to solve this optimization problem: min $\sum^{N}_{i=1}x_i$, with the following constraints: $\sum^{N}_{i=1}\frac{b_i}{log_2(1+\frac{x_iz_i}{s})}-T\leq 0$ $00$ for $i=1,\cdots, N$, and $s, T, X >0$ are all known…
Garbt
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Keyword describing optimization problem of repeated function evaluation

Consider some function $f(x,p):\mathbb{R}^6 \times \mathcal{D} \subset\mathbb{R}^n \to \mathbb{R}^6$ which transforms vectors $x$ in dependence of parameters $p$. The evolution of $x$ is given by $ z = \begin{bmatrix} f(x, p) \\ f(f(x,p),p) \\…
Tengrath
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Trying to write a formalization for an optimization problem

Write the optimization problem that allows you to find the minimal distance using the Euclidian norm, between a polyhedron {x ∈ R^n : Ax ≤ b} and a hypersphere of center in $x_{0}$ and radius δ. It can be formulated as follows: Minimize: $ d = \|…
Scipio
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Example of places where argmin is more important than the minimum itself?

Clarification: the word "important" is ambiguous. Here, I use "important" to mean that we want to know the value of a quantity accurately. For many optimisation problems, it looks as if we are more interested in finding the minimum value, rather…
Ma Joad
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Minimization using the penalty method

I dont understand what was made between step (1) and step (2). How did they managed to get to (2)? I tried solving both equations in order of x1 and then solve the equality to find x2 in order of p but i dont get the same thing.
Scipio
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How to solve an inequality with supremum, a function containing arbitrary constants?

I have an inequality as below, and I need to find the solution set of this inequality. I couldn't find a method on how to solve it. It would be great if I could find all the $L_1$ and $L_2$ values that satisfy the inequality. There are conditions…
Burak
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Optimizing the number and placement of valves in a pipe network to meet requirements

If you have ‘n’ components connected via piping, and ‘m’ modes of operations that dictate how fluid flows between the components in each mode, is there an algorithmic way to optimize how many multi-port valves with ‘x’ ports are required to satisfy…
Wayne King
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Seeking More Efficient Solutions for a Discrete Optimization Problem

I'm an engineer with not-so-strong mathematics skills. My apologies if my title is misleading, as I am unsure how to properly categorize this issue. I came across a practical problem at work, described as follows: $a$, $b$, and $c$ are nonnegative…
yamiew
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Minimum-time C2 Continuous Velocity Profile Optimization

Given limits for velocity, acceleration and jerk, $v_{max}(x)$, $a_{max}$ and $j_{max}$ respectively. The goal is to generate a velocity profile that obeys the limits and minimizes the time / maximizes the velocity. In the case where jerk is not a…
fullnitrous
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Optimization of an expression using partial derivative

Find the maximum value of $\sqrt{x^2+y^2}$ where $$x^2+y^2=6x-8y+11$$ where $x,y$ are real numbers. Now one approach is just to write the given expression as the equation of a circle, and the maximum value of $x^2+y^2$ would be the distance…
Ellie_Wong
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When can tri-level optimization be written as bi-level optimization?

I conceptualize a following tri-level optimization problem: $$ \begin{aligned} & \min_{x_1,x_2,\theta} \ell(x_1,x_2) \\ s.t. \quad & x_2\in\arg\min_{x_2}\{\ell_2(x_2): \\ & \qquad g_2(x_1,x_2)\leq0 \\ & \qquad x_1 \in…
TedWXu
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heuristic optimization of a complex function

Here I am giving a heuristic scheme based on an engineering point of view. We have a very complicated function P(X,Y,Z,U,...) involving any type of expression such as log, polynomial, square root, inverse, etc. Now we want to minimize this w.r.t…
A.Soleimani
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Travelling Circle Problem (how to find the shortest path by drawing unit circles?)

(This is a variation of the Traveling Salesman problem.) Define a point $P_0$ at the origin. Define an "iteration" by putting a circle of radius $1$ around $P_0$ and choosing any point with real coordinates the circle. Let that new point become…
Infigon
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