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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Maximizing $7x+12y$ over the set $2x^2+6xy+9y^2-2x-6y\le 24$

By bounding the function, I need to find the maximum point of $7x+12y$ over the set $2x^2+6xy+9y^2-2x-6y\le 24$ (i.e., no Lagrange multipliers are allowed, etc.). I am trying to show that $(7x+12y)^2\le C$ for a constant $C$. Then I will search…
MasterJ
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line fitting with numerical optimization

I'm programming a small MATLAB project to fit a 3D line to a line cloud point having N points using optimization technique, currently steepest descent and BFGS (working). The problem is described by the figure: Premise: a point that estimating…
Shawn Le
  • 289
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maximize $-\sum_{i=1}^n \log \left( \lambda_i + \kappa \right) - \sum_{i=1}^n \frac{c_i}{\lambda_i + \kappa}$

Trying to find the maximum of a log-likelihood, for a parameter in a covariance function. I end up with the following problem, that should be concave if my calculations are correct, \begin{align} &\max_{\kappa}\; -\sum_{i=1}^n \log \left(…
Jonas Wallin
  • 316
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Number grouping and minimizing the maximum absolute deviation

I have a problem for which I am trying to produce an efficient algorithm. I tried to do a literature search, but I kept getting results for similar problems, never getting what I really want. Could you point me in the right direction for putting a…
Hodin
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Distance between two airplanes that are NOT at 90' angles

At noon on a certain day, a plane is $200$ miles south of another aircraft and flying north at $550$ mph, while the second plane is flying southwest at $600$ mph. How much later after this instant is their distance a minimum? I can easily work this…
user147485
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find minimum of a function with abs and squares analytically

maybe someone here can help me. I want to find the analytical minimum '$x_\mathrm{opt} = \arg\min f(x)$' of the following function: $$ f(x) = \alpha |c + x| + \beta x^2 $$ where $x$ is a real number ($x$ is_element_of $\mathbb{R}$), $c$ is a real…
Richard Hoepfelsson
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Is there any better expressions better than what I propose?

Let $\mathcal{S}\subseteq\mathbb{R}^n$ be a set of an inaccessible area. We consider the time as $\{\ldots,~ t-1,~ t,~ t+1,~ \ldots\}$. We assume that a position of a point at time $t$ is given as $x\in\mathbb{R}^n$, and its position will be changed…
Danny_Kim
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Minimum cost of a rectangular closed storage tank

A company wishes to construct a rectangular closed storage tank with a square (horizontal) base. The tank must have a fixed volume of 100 cubic metres. Find the dimensions for the minimum cost of material; a. If metal for sides and top costs…
William
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Can somebody please explain the sequential tree-reweighted message passing (TRW-S) algorithm

I desperately need your help. I have to understand the sequential tree-reweighted message passing algorithm proposed by Kolmogorov [1] for energy minimization. I tried to understand it, but I have no real "Aha moment", so I hope that someone of you,…
Tukk
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How do find the optimal values for these expressions?

Say I have three constants a, b and c (all > 0) and three variables x, y and z (all >= 0). I want to find values for x, y, z which maximise the lowest of the following: ax - y - z -x + by - z -x -y + cz How can I find these values? EDIT: just…
user7694
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Please suggest an asymmetrical objective function based on a distance measure?

I have an optimisation problem where I wish to find the fitted values $(\hat{y}_1, \hat{y}_2, \dots, \hat{y}_n)$ that minimise a pairwise 'distance' to observed values $(y_1, y_2, \dots, y_n)$. I would like to penalise negative distances more than…
Alex
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A question from the laboratory

I had this test in my neuroscience laboratory, and we had all sort of brain tissue spread in front of us. Each one had multiple needles attached to it with numbers on them (marking places I needed to answer how they are called). So apparently the…
Ido Kessler
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Reduce Global Optimisation Search Domain

I have an optimisation problem for which the objective function is not differentiable. I am looking for a global optimum using the Simulated Annealing technique in MATLAB. I am facing the problem of a very large search domain. I want to narrow down…
user14352
  • 119
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Smallest number of steps to reach from X to Y

You are provided a number X and another number Y. You can apply only the following operations : - a) If the number is even, either double the number or increase it by 1. b) If the number is odd, either double the number or decrease it by 1. What…
user249117
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When is Sequential Optimization = Simultaneous Optimization?

My objective is to maximize $f(x,y,z)$ subject to two constraints $g_1(x,y,z)=0$ and $g_2(x,y,z)≤0$. (There is an Econ story in the background). For simplicity, I use the following sequential optimization method. First I fix some $z$ and…
Salim Kurt
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