Questions tagged [maximum]

Questions on finding the largest value of a set, extreme values of an expression, or on Mathematica functionality for maxima testing.

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Polynomial approximation of max function

Let me just say upfront I'm not a mathematician, I'm rather looking for a practical answer to my question. I was wondering if there is a polynomial approximation for the function $$\max(0,x)=\left\{\...
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3 votes
2 answers
73 views

Why does Maximize return this unevaluated?

Maximize[{PDF[NormalDistribution[0, sigma], x], sigma > 0}, x, Reals] Just returns unevaluated (when, obviously, it should return ...
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0 votes
0 answers
78 views

Maximization Problem

I am trying to find the solution of the following problem. $ \max_{n_{\in [1,M]}} \frac{n \left(\frac{k (n-2 (\rho -1) \tau )}{\frac{k n (n-2 (\rho -1) \tau )}{2 (n+1)^2}+1}-2 \rho (\tau -1)\right)}{...
  • 38
0 votes
2 answers
57 views

How do to create 3D plot for the argument from two another arguments for maximum of the function?

How do to create 3D plot of ${t_{opt}} = {f_2}\left( {x,y} \right)$, where ${t_{opt}}$ is corresponding to maximum value of ${f_1}\left( {x,y,t} \right)$ at the limited ranges of $x,y,t$? If $t$ ...
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0 votes
1 answer
79 views

Maximization of a concave function with contraints in the arguments

I have been struggling on solving this problem. Suppose you have a function f(x, y) that is concave in x and y. I want to find (x, y) that maximize f(x, y) with x ...
  • 41
0 votes
0 answers
30 views

Evaluation stops without output or error when using Nested Maximize

I am trying to evaluate a max max min problem. The code is as follows: ...
-3 votes
1 answer
46 views

Maximum number of routings for n points [closed]

I'm trying to formulate an equation to calculate the maximum number of routings possible for a given amount of points, with the following rules or restrictions: A route must contain atleast one point ...
1 vote
2 answers
121 views

Why can't I get the maximum value?

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3 votes
1 answer
124 views

How can I find the maximal value of this?

I already plot the image of the function S: ...
  • 381
0 votes
0 answers
42 views

How to find the positive maximum value of this total profit function?

So I have this function and I want to find the maximum value and the plot for x I'm not really sure if I wrote the integral function correctly in mathematica, but here is the code I attempt : ...
2 votes
4 answers
275 views

From original dataset, find the probability of each element in each row having the maximum value in its row

Suppose I have this dataset {{1, 3, 5}, {4, 4, 2}, {5, 3, 5}, {10, 4, 10}} // MatrixForm How do I find the probability that each cell is the maximum in its row. So ...
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1 vote
1 answer
75 views

Find binary vector within fixed distance to reference vector that maximizes the number of distances to a set of vector that are below a threshold

Input: A binary reference vector $r$, a multi-set of binary vectors $S$, and a distance function d between binary vectors of equal length. Assume that $r$ and all vectors in $S$ have the same length. ...
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1 vote
2 answers
56 views

Find min value of a complex Root function [closed]

Could someone tell me how to obtain the min value of this function when lambda is between 0 and 1: ...
  • 11
3 votes
2 answers
129 views

Find global maximum of InterpolatingFunction in interval but not maximum value

I have InterpolatingFunction generated from experimental data with many local maxima, one major peak I need to find, and the tail that grouse much higher then major peak. I tried to find my peak with ...
2 votes
1 answer
94 views

Parametric minimization of a quadratic expression in two variables

I am not an expert in using Mathematica, and I do not understand the following result (apologies if it appears trivial). I want to find the general solution to minimize the following expression over $...
4 votes
1 answer
93 views

Find the minimum & maximum and plot it with the mean data

Hi I have ten data set and manage to calculate the mean using them. However I hope to find out the upper and lower limit in each point and plot it out with the mean data. May I ask how can I ...
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1 vote
2 answers
324 views

How do I find the minimum and maximum values of a function of two variable with constraints? [closed]

The question is find the minima and maxima of the function $$f(x,y)= x^2+5y^2+11x-12y+30$$ on $(x^2)/81+(y^2)/49 \leq 1.$ I've been trying to use FindMaxValue and <...
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3 votes
1 answer
74 views

Finding maximum of 2D interpolating function as a function of one of the variables

I am solving a 2D PDE in space and time b(r,t) and would like to find the maximum value of b in space as a function of time t. Using the solution for maximising a 1D interpolating function from here, ...
0 votes
0 answers
58 views

extremum points

I'm trying to find Min and Max points of the polynomial below, but it seems that the expression is very complicated to mathematical, I've tried a numerical function, such as NMinimize, NRoots, Solve, ...
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0 votes
0 answers
36 views

How to obtain the most accurate maximum value of the given equation? Changing WorkingPrecision gives different results

I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1.56 <x< 1.6$ and $3<y<\pi$. ...
  • 659
0 votes
2 answers
118 views

How to calculate the maximum value of $x $ which satisfy the conditions $g(x,y)=0$ and $f(x,y)>1$?

I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
  • 659
0 votes
2 answers
105 views

Find maximum value of a function - wrong output? [closed]

I want to find the local maximum value of the function: where the domain is 0 < x < 3/2. Wolfram|Alpha gives me the correct answer while Mathematica gives me a totally different answer. Why is ...
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1 vote
0 answers
79 views

Full Information Maximum Likelihood - Under some other name in Mathematica

I have recently stumbled upon something called FIML - Full Information Maximum Likelihood. Apparently this methodology helps overcome missing variables provided the gaps are random. Searching the ...
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3 votes
2 answers
96 views

Argument of maximum value of a table in range

I have data = {{817, 501}, {818, 549}, {819, 562}, {820, 534}, {821, 534}, {822, 535}, {823, 516}}; How to find argument "822" for 535 (which is the ...
-3 votes
1 answer
52 views

Maximize function problem [closed]

I don't understand why I'm getting no solution with the Maximize function in this case: while it returns the right result when I impose $y\leq0.999$ (or, equivalently, $x\leq0.999$):
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0 votes
2 answers
117 views

NMaximize - global maximum fail - How to?

Problem : Let x,y,z be non-negative real number whose sum is 1. Find maximum of 0.2x + 0.2y + x^2*z + y*z^2 What I did first was reducing variable. ...
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0 votes
0 answers
104 views

How can I set a find max value function with parameter in NDSolve

For example, Here is a NDSolve function with a parameter of w ...
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2 votes
3 answers
288 views

Finding the Global Minimum

Consider the function ...
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0 votes
0 answers
62 views

NMaximize computes wrong value

This question is a continuation of NIntegrate with a complicated function over the 4-sphere . Now I define a certain new function called "improvement" via: ...
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1 vote
1 answer
86 views

Function range with numerical method

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3 votes
2 answers
364 views

Polygon Diameter

I want to calculate the diameter of a convex polygon. That is, the largest distance between any pair of vertices. Here's my approach ...
  • 4,330
0 votes
1 answer
85 views

Maximization under constraints / find maxima

I am trying to code the following maximization program that I am not able to solve algebraically (Of course I manage to get the first derivative, but struggle finding its root): $\begin{equation} Max_{...
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3 votes
4 answers
488 views

How can I mark the maximum value in a plot?

How can I mark the maximum value in a graph? The graph that I would like to determine its maximum value, is an output of the following program: ...
0 votes
1 answer
98 views

NIntegrate allegedly evaluating to non-numerical values

I'm getting non-numerical-evaluation error messages despite not having any symbolic variables in my code. Here's a MWE representative of what I'm doing: ...
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0 votes
0 answers
30 views

How do I get actual solutions from MaxValue?

Say I want to calculate the maximum value of a simple function of two variables: f[r_, t_]:= r Cos[t]^3 (1 + r Sin[t]) with respect to the variable ...
  • 548
1 vote
3 answers
134 views

Maximize - Non binding constraint is changing the result

When I add a non-binding constraint to a maximization problem the result changes. I don't understand why. Below you can find the code that I am using. For the maximization A, H = 6837.66 For the ...
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2 votes
0 answers
63 views

How to best compute the maximum value of a multivariable function?

I'm new to Mathematica. I have the function: ...
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3 votes
2 answers
110 views

Syntax error in NMaximize despite following official documentation

This is the code I'm trying to run: ...
2 votes
0 answers
87 views

Maximize a function over complexes

Assume that I have a bounded real valued function $h(a,b)$ such that $a\in \mathbb{C}$ and $b\in [0,1]$. Can Mathematica maximize such function over $\mathbb{C}\times [0,1]$? I tried some functions ...
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0 votes
1 answer
40 views

Unable to formulate the correct formulation for maximize a function

So, i want to express these: $$\max(\cos(x)\cos(y)\cos(z)),\quad x+y+z=\pi,\quad x,y,z\in(0,\pi]$$ Attempt: ...
1 vote
1 answer
68 views

NMaximize seems not to work with a plottable function

I am trying to use maximum likelihood for estimating a parameter for a model based on some experimental data. The likelihood function I am trying to maximize calls a number of custom functions I have ...
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1 vote
1 answer
52 views

Find maximal elements of list (remove dominated elements)

Suppose I consider a to be greater than b if a[[1]] >= b[[1]] and ...
  • 1,073
6 votes
2 answers
204 views

Find largest and second larges number in each row and column

I am trying to find the largest and second largest number in each row and column. The largest numbers are easy, but how do I find the second largest? After I found them I also want to calculate the ...
7 votes
2 answers
628 views

Is it possible to ask Mathematica to give the maximum value of a function over a specific domain?

I have a function $f(n)$ over $n\in\mathbb{N}$. I want to know its maximum value over a very large domain, say $n=1,2,3,4,...,10^6$. Is there a way to ask Mathematica to give me the maximum value of ...
  • 1,159
3 votes
4 answers
480 views

Nested optimization problem - Function approximation

I need to maximize the following function (the input to NMaximize below) ...
2 votes
2 answers
110 views

How to find maximum of two or more parametric functions?

I have two parametric functions in which I know the range of parameters and I want to find the maximum of these two functions by conditions on the value of the variable. Suppose $f(x)=x-c$ and $g(x)=r....
  • 147
4 votes
2 answers
190 views

Maximum of all distances between any pairs of vertices of a random triangle

Given a set $S_n$ of $n$ points selected uniformly at random in a $d$-ball, I want to estimate the average length of the longest side of a triangle having as vertices any three distinct points of $S_n$...
1 vote
1 answer
108 views

How do I find the maximum of a certain complex expression? [closed]

I have this expression: TFilter1 = -(7.5438*10^8/(6.34731*10^8 + 48270.2 s + s^2)) where s is a complex variable give by $s = ...
0 votes
0 answers
35 views

Finding/Printing Variables that Correspond to the Maximum Output of a List

I am very new to Mathematica and been having a problem that is frustrating because I feel that there must be a simple solution which I just can't grasp. Essentially, I am looking to automatically ...
  • 1
0 votes
1 answer
71 views

Maximize a simple expression based on EuclideanDistance takes too long

Do you know if there is a mistake in this command syntax? It is very simple and still it takes too long. I cannot obtain any result at all: ...