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").

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Minimize sum of product of series, given constraints

Given a series $x_t$ and constants $c_1$, $c_2$, I want to find another series $y_t$ such that $\sum_t x_t \cdot y_t$ is minimized, and $\begin{cases} 0 < \sum_s y_s < c_1 \text{ for all } s \in 0..t\\ -c_2 < y_t < c_2 \end{cases}$ What kind…
Pibben
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$\max F(u)=\min G(u)$?

Let $a>0$ be a fixed real number and consider the semi-circle $y(x)=\sqrt{(a/2)^2-(x-a/2)^2}$ for $x\in [0,a]$. Let $Y=\{u\in C([0,a]):\ u(0)=u(a)=0,\ u\geq 0,\ \ell(u)=2a\}$, where $\ell(u)$ denotes the length of the graph of the curve. Consider…
Tomás
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Looking for papers / terminology on binary array guessing game problem

a. Alice thinks up an array of N binary numbers b. Bob guesses an array of N binary numbers c. Alice responds only with ONE number, which is the number of binary numbers in the correct position An alternative to this problem is…
Blaze
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Given a finite set U, how can we enumerate all subsets of U that have an odd number of elements

That is pretty much this, given a finite set U, how can we enumerate all subsets of U that have an odd number of elements? This is a question about enumaration on my optimization subject and I really don't know where to start
deidara
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This set minimize the minimum?

Let $S$ a finite set and let $A \subseteq S$ and $B \subseteq S$. We can say that $Z = B$ minimize the following minimum: $$\min_{Z \subseteq S} \{|A \cap Z| + |B-Z|\}$$? If yes, why?
Frank
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A simple manufacturing problem

Suppose we have several stations. In each station there are several operators. Each operator conducts several tasks during one cycle. Each of the tasks requires (several) materials. Materials are delivered in material containers with a certain size…
Sebastian E
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Lagrangian dual in continuous domain

The continuous max flow problem is posed as follows : sup $\int_\Omega p_s(x)dx$ subject to : $|p(x)| \le C(x); \forall x \in \Omega $ $p_s(x) \le C_s(x); \forall x \in \Omega $ $p_t(x) \le C_t(x); \forall x \in \Omega $ $\nabla \cdot p(x) -…
AnkurVijay
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Block Coordinate descent (BCD) a gradient-free method

in "Global Convergence of Block Coordinate Descent in Deep Learning" the authors claims that BCD is gradient-free method but in "Block-Cyclic Stochastic Coordinate Descent for Deep Neural Networks" authors calculate the gradient in the BCD…
Shazia Riaz
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Syntax check for an l2 optimization

$f[m]$, $g[m]$, and $c[m]$ are three distinct discrete-time functions. I want to find the coefficients of $f[m]$ such that the l2-norm of error (defined as $f(m)* g(m)-c(m)$) is minimized. Is this the correct representation in the…
dsp_guy2020
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Having trouble reading this formula

Please help me translating this formula to plain english. I have no idea whats happening here $$ \{x^{(k)}\} \subset X, x^{(k)} \rightarrow x^* \in X \Rightarrow \liminf_{k\rightarrow\infty} f(x^{(k)}) \ge f(x^*) $$ Thanks in advance
user2762996
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How to maximize $\sum_i^n 1/2^{v_i}$

How to maximize $\sum_i^n\dfrac{1}{2^{v_i}}$ where $, v_i\in \mathbb{N}$, $0\leq v_i
juaninf
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Defeinition of robust counterpart in robust optimization

I'm working on robust optimization problems and trying to summarize a bit about some basic ideas. However, one really confusing thing is the definition of a robust counterpart. Definition 1.2.5 from Ben-tal's book, says \begin{equation} \min…
zzgsam
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What is the mistake in my approach and how to rectify it?

Is this possible to solve without partial derivatives? in this i asked about to find minima of the function $f(x,y)=\sqrt{x^2-14x+74}+ \sqrt{y^2-4y+20}+ \sqrt{x^2+y^2-10x-10y+50}$, this is my progress by considering two fixed points in cartesian…
Paracetamol
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Is there a way to minimise a function and maximise another at the same time?

Say I have two functions of the variable x, f and g. I would like to find a single value of x that gives me the largest value of f and smallest value of g. Is there a procedure to do this? Note: I'm not talking about the global maximum of f and…
ranky123
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Modelling: Word to maths and solutions

I have a general problem in going from a problem that is described in english to it being described in mathematics and then solving it to find the solution. Take, for example, that I have a set of "houses" with features such as {bedrooms,…
hairybear
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