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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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Optimization of a black-box function made of step-functions

I need to optimize a function $f:\mathbb{R}^n\to\mathbb{R}$ of which the explicit form missing, but I can evaluate it at any point of its domain. The only thing I know is that such function is piecewise constant. Also, the evaluation of the…
the_elder
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Joint optimization for three variables that are not separable

I am looking for a way to optimize F(x,y,z) = f(x) + g(x,y,z) + h(x,y,z) with respect to three vectors x,y,z to where f, g, h are given by f(x) = ||d – Px||^2_2 g(x,y,z) = a*||z – B(y)x ||^2_2 h(x,y,z) = b*||Ax + B(y)u +z||^2_2 Knowns for this…
GoodGame
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Maximum of continuous non-smooth function over an interval

Suppose that a continuous function $f: \mathbb{R} \mapsto \mathbb{R}$ is non-smooth, but has a single maximum on the interval $[a,b]$. Inspired by Riemann integrals, I started to consider $$\lim_{n \rightarrow \infty}\max \left( f(a),…
Galen
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Is this constraint a special case of signomial programming?

I am a post graduate student in Electrical Engineering and I am working in optimization. Suddenly, I was running into a situation where my problem has a constraint in the form of $${x_1}{x_2}{x_3} - \left( {\frac{1}{3}{{\left( {{x_1}} \right)}^3} +…
Tuong Nguyen Minh
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Finding a minimum route on a chessboard

I'm not sure if this problem fits here. Consider a rook taking a tour on a chessboard with a number of squares blocked (see attached figure). Here, our rook started in the upper left corner and visited each square once in 23 moves. But what starting…
Ken Bannister
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Solution to a scarce resources assignment game

I would like to tell you about this game, which can looks like very simple but there's a constraint which complicates it and prevents me from finding an analytical solution. Rules of the game: there are two types of points, called "Points A" (or…
Lisa Ann
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Optimization problem: Find the shortest path between a set of modules

We want to connect $n$ modules by wires. The distance between two position $i, k$ is $a_{ik}$. $b_{jl}$ is the number of connections between module $j$ and $l$. Now we're looking for an assignment of the modules to their positions so that the total…
illuminatitruthseeker
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nonmonotone line search-Why might a non-monotone line search not be satisfied

The line search criteria are as follows: Parameters $\lambda_1$, $\lambda_2$, $\sigma$, and $\delta$ are introduced where $0 < \lambda_1 < \lambda_2$ and $\sigma, \delta \in (0, 1)$, and they set $\alpha_k = \overline{\alpha_k} \sigma^{h_k}$ where…
user20554950
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Differential equations phase diagram

I am trying to create a phase diagram of two differential equations. (This is an optimization problem, so I am using state(s) and control(c) variables w.r.t.…
Petar N Neychev
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How to solve max min (convex functions)?

I am trying to solve the following optimization problem. $$ \max_{A} \min_{i,j,i\neq j} ||A(x_i-x_j)||_2^2 \\ \text{s.t } ||A||_F^2 <=1 $$ $A$ is a matrix and $x_i$ are given vectors. The min of convex functions is not a convex/concave function. Is…
dsp_guy2020
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What optimization model is used to divide groups of objects with feature according to some coefficient and percentage?

We have N groups of objects. Objects could be triangles and rectangles (it's just an example to generalize question). Number of triangles and rectangles are not the same. Each group contains $r_{i}$ - rectangles, $t_{i}$ - triangles, so overall…
Nikita Artemenko
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How to tell whether you've found the minimum number sent to the first that also maximizes the candy sent to the first person?

16 children are standing in line to receive a total of $100$ pieces of candy, with each child guaranteed to receive at least $1$ piece. At (leas) how many pieces must the first child in line receive to ensure that he or she has the greatest number…
user685056
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How to find constraints of optimization problem using first order condition?

I am studying past exam answers for a remote econ math exam, but I don't understand the given solution for this question: $$ \begin{array}{ll} \text{Maximize}& z(x,y) = y e^{5x} \\ \text{Subject to}& ax + by = 8 \\ \text{Where} & x\geq…
noblearistocrat
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Is it possible to solve the steepest ascent method with the initial point (0,0)?

I have a function $g(x,y) = 1-(xy-3)^2$. Starting at $(x,y) = (0,0)$, is it possible to apply one step of the steepest ascent method to the problem $\underset{(x,y)\in R^2}{max}$ $g(x,y)$. The gradient I've obtained is $\triangledown g$ =…
TM1
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Optimization Problems and 13th Century Norwegian History

Consider this example: Suppose you have to take an exam about Norwegian History in the 13th Century and you know absolutely nothing about this topic. You have the choice between taking an exam where all the questions are either TRUE/FALSE or an exam…
stats_noob
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