Mathematics Stack Exchange
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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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Multi objective optimization: Ideal vector

I'm going to consider the two problem distinctly. Now I want to calculate $z_1^{id}$ and $z_2^{id}$ and $x_1^{id}$ and $x_2^{id}$ where $z_1^{id} = min(x)$ $z_2^{id} = max(y)$ $z_1^{id}$ is the value of the first objective function when I…
user1028100
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Is there a name for this type of online optimization problem?

I have a sequence of items $1\leq i \leq n$ that arrive to me one at a time. Each item has a weight $w_i\geq 0$. If I pick up one item, I will not be allowed to pick up any of the next $k$ items ($k< n$). The question is: how can I optimally pick up…
spica
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E-olymp: Cake. Giving Wrong Answer

Cake This is a e-olymp programming question mathematical optimization. In honor of the birth of an heir Tutti royal chef has prepared a huge cake, that was put on the table for Three Fat Man. The first fat man can eat the cake by himself for t1…
Black Bird
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multi objective optimization

Suppose we want to maximize two positive bounded objectives. A usual approach for this aim is to maximize a weighted sum of these two objectives. Now, my question is why not to maximize the product of these two objectives? Are there any…
user1936314
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How to optimally cut kitchen worktops (countertops) from slabs of material

Given a number N of rectangular kitchen worktops, of variable dimensions to be cut from slabs of material of fixed dimensions Determine an optimal fit to minimise wastage and number of slabs used. Two refinements to the problem are: 1. Slabs may be…
Andrew Bingham
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optimization function

If we want to maximize a function $f$ and we know that $f$ depend on 3 variables $v_1$, $v_2$ and $v_3$ without knowing the exactly relation between them but we know that maximizing $f$ can be achieved through maximizing $v_1$ and $v_2$ and…
MahopeRam
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Maximising an area

I was wondering if someone could possibly explain this question: "A stadium should be oblong on plan with straight sides of length h and semi-circular arcs of radius r at either end. The facade must be 10m high all the way around and as such it…
S Hayward
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Maximization problem with constraint: no differentiation

$$\max \ \min[\alpha x_1, \beta x_2, \gamma x_3] \ \ \text{s.t.} \ \lambda_1 x_1 + \lambda_2x_2 + \lambda_3x_3 = c, \\\ \alpha, \beta, \gamma, \lambda_i, c \ \text{are constants}$$ Well, that function is not differentiable , so what methods can be…
Mikaela Deynfueu
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Proving the existence of multiple maxima

Given a function of two variables, say f(x,y), what are some known techniques to prove that it has multiple maxima? I can see via simulation that this is the case, but trying to figure out a formal way to do so.
Dhiraj
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Devising a likelihood method for estimating disease prevalence in hunted deer populations

I am attempting to find the maximum likelihood estimate for disease prevalence in trapped mice by using data on the probability of being trapped each year and the number of mice actually trapped that year. Imagine a group of juvenile mice. There is…
ZombiePlan37
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How can a function of the form $\sum \sum \frac{\lvert x_{i} - x_{j}\rvert^{p}}{p}$ be minimized? (Part I)

This is part-1 of a series of questions regarding (ultimately), in my implementing a co-ordinate descent algorithm, but I have broken it up into parts as I try to solve it 'by hand' first, so that I can better understand. So basically, I am given a…
Spacey
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Maximization of a function I came up while studying

So in a problem I am trying to solve, after calculations I came up with the following function: \begin{equation*} f(\overline{y},\theta)=\frac{e^{n\,min\{\overline{y},\theta)}-1}{n\theta} \end{equation*} where $\overline{y}$ a vector of dimension…
SpawnKilleR
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Find maximum and minimum of funсtion on set

I have the task: find maximum an minimum of $$f(x) = x_1(\pi - x_1)\sin x_2 + x_2 \cos x_1$$ on X where $$X = \{x\in R^2\ |\ x_1\in [0, \pi], x_2 \ge 0\}.$$ First thing i did was system : \begin{equation*} \begin{cases} \frac{\partial…
Simankov
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How to do optimization

My teacher gave me a very complicated explanation on how to solve an optimization problem so I just wanted clarification. To do so I have laid out what I think is the simplest way to solve it. Take the derivative of the function given. take $f'(0)$…
alex
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optimization for the area of a garden

I have been working this problem for awhile and cannot seem to solve it even though its probably easier than I think... There is a rectangular garden that needs fencing. For one side of the fencing wooden slats will be used costing 2 dollars per…
alex
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