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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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24 views

FindMaximum + NMaximize + Arc of the Cycloid?

I am graphing the parametric equations for the arcs of the cycloid (common, curtate, and prolate). This equation works well: ...
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42 views

difference between max() and max^(0,1)

I have a really complicated function that I need to take partial derivative of. After executing the partial derivative, I got a function that contains both $\max(0,a-b)$ and $\max^{(0,1)}(0,a-b)$ for ...
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35 views

Maximize violate constraint of non approximated function

here is my code Maximize[{-(10/17) - x + (20 (1 + x))/(17 (2 + x)), 0 <= x <= 1.5}, x] The result I got: {6.66134*10^-16, {x -> -9.79755*10^-16}} As you ...
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61 views

Next maximum plot with results from NDSolve

I want to produce a Next-maximum-plot, i.e., I want to plot all local maxima $m_{i+1}$ against the local maximum $m_i$ in order to check for chaotic behavior. In particular, I have the following code:...
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69 views

problem with maximize function and envelope function

I Have the problem with the maximize of this problem: ...
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63 views

How do I find all maxima of this function?

I have to find all the maxima of the function fun[t_?NumberQ] := NIntegrate[1/y^(11/3) Cos[y t], {y, 1, 2 }] To find the poit with zero first derivative I have ...
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17 views

Problem with PiecewiseExpand[Max[ ]]

I have these functions: By running this command: FullSimplify[PiecewiseExpand[Max[a, b , c, x, y, z]], 9 <= \[Beta] <= 11] I obtain: However I think ...
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3answers
34 views

Highlight largest value in each column of `Table // TableForm`

I am exploring colossally abundant numbers; in particular the set of specific 'critical epsilon values'. I table the function DivisorSigma[1, n]/n^(1 + \[Epsilon]) ...
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1answer
51 views

Maximization of a a PiecewiseExpand funcion

I have the following 3 piecewise functions and their upper envelope. ...
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3answers
159 views

Optimising the Selection of MaxValue in Association

Suppose I have the following Association: ...
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4answers
90 views

Sorting polynomials based on their y value and finding their intersection

I've got the following list of polynomials, ...
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0answers
70 views

How to differentiate a function constructed through FindRoot?

I am trying to maximize a function which has as a variable another function that was solved numerically using FindRoot. My code is below.I start by defining some parameters ...
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1answer
46 views

Sorting an Association by FindMaximum

Prompted by my wrestling with this earlier question: Changing the opacity of lines on a plot based on their value I want to sort an association by the maximum value for each of the 3 members of the ...
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1answer
31 views

Linear Programming using Maximize

I am trying to solve a more complicated version of the following LP problem: I have some constraint amounts a,b,c and two variables made of those amounts. I would like to find the best way to ...
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1answer
93 views

Given a function $f(t,s)$, compute $\max_{t_2\in [0,1]}\min_{t_1\in [0,1]} |f(t_1,s_1)-f(t_2,s_2)|$

Given a continuous and bounded function $f(t,s)$, $t,s\in[0,1]$, I would like to compute $$\max_{t_2\in [0,1]}\min_{t_1\in [0,1]} |f(t_1,s_1)-f(t_2,s_2)|,$$ for each numeric values of $s_1$ and $s_2$....
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2answers
86 views

Find the max value of $f(x,y)= 9\ln(x^2+2y^2+1)-x^2-y^2$

I need to find the max value of: f[x_, y_] := 9 Log[x^2+2y^2+1] - x^2 - y^2 which has a center at the origin and radius 4. Maximize and NMaximize are not working ...
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372 views

How can I get exact maximal value of this expression?

I am trying to find the exact maximum value of the expression $$ E= \sqrt{5 a^2+a (4 b-2 c)+2b^2+4 b c+5 c^2}+\sqrt{2a^2+a (2 b+2 c)+2 b^2-2 bc+2 c^2}+\sqrt{26 a^2+a (10c-2 b)+26 b^2+10 b c+2 c^2} ,$$ ...
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1answer
60 views

ArgMin and NArgMin gives different result

Im doing the same problem with ArgMin and NArgMin, however NArgMin messes up the order of the solution. Given function: ...
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2answers
65 views

Parametric Find Maximum

I'd like to plot the maximum of a curve in function of a parameter. Meaning I looking for maxima that depend on a parameter. Here is what I tried to do but FindMaximum is not parametric, so it did ...
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1answer
45 views

Finding two peaks of a plot (dataset)

I have a dataset which on plotted looks like the following: As you can see there are two maximas around origin, I want to find out the (x,y) value of both of them, is there a way to do so?
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3answers
78 views

Plot maximum value of a function of three variables

Given a function f[\[Theta]_, \[Phi]_, t_] given by ...
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0answers
38 views

NMaximize with a variable ranging over permutations

I have an optimization problem where there are $n$ activities and I want to find an optimal schedule of those activities. The schedule is specified as $S=(\mathbf{t},p)$ where: $\mathbf{t}=\left(t_{...
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1answer
71 views

Maximize and FindMaximum drive me crazy

I have to run a numerical study. As part of it I have to solve: ...
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26 views

Using MaxValue to define a function, plotting is slow

I'm trying to compute c-functions (from the theory of optimal transport), and so I must compute `supremums' for some function $f$ and cost $c$ $$g(y)=\sup_{x\in \mathbb{R}} c(x,y)-f(x)$$ My code ...
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2answers
41 views

Unable to find maximum value of my custom function

myfunn[x_, y_] := Module[{}, If[x < 5, Return[0]]; If[x < 10, Return[2]]; x*y]; I'm unable to find the maximum value of this function over the ...
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2answers
160 views

NMaximize is not converging to a solution

I am trying to use NMaximize to find the maximum value of a variable that satisfies the given constraints. Since the constraints aren't straightforward, I am using ...
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1answer
94 views

Problem with constraints of NMaximize

I am using NMaximize to solve the following problem. ...
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1answer
46 views

Maximize function subject to condition [closed]

What commands should I use in Mathematica to obtain the maximum or minimum of a function subject to conditions? For example, find the maximum of the following function? $\qquad T=\sqrt[3]{2\,x+5} + \...
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74 views

Find the maximum of a function involved with Floor function

My function is $$ f(H,p) = \left\lfloor \dfrac{\lfloor H/p\rfloor + 3 - \sqrt{(\lfloor H/p\rfloor + 1)^2 - 4H}}{2} \right\rfloor $$ The constraints are $ H \geq p(4p-1) $, $ p $ is prime although ...
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2answers
47 views

Define x as a multiple of a number as a constraint in the Maximize function

I am trying to optimize a linearly constrained Production Function. I have three inputs and want them all to be multiples of 150. I can make all the inputs to belong to the Integer Domain but is there ...
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1answer
143 views

How to do Maximum Likelihood Estimation with this Multivariate Normal?

I'm trying to perform Maximum Likelihood Estimation, where the data follows a Multivariate Normal. The problem, I think, is that in the density, we have the inverse of the covariance matrix. This ...
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2answers
133 views

Finding a maximum on a plot

My script is currently: ...
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0answers
60 views

NSum: Summand (or its derivative) is not numerical at point

I am experiencing a problem in evaluating the maximum of a function that is defined as a sum ...
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1answer
131 views

Periodogram local maximum

I want to find dominant frequencies of periodogram exactly. ...
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214 views

Automated searching for maximal 2D point configurations

I have some black-box function that takes lists of 2D points, and I would like to find some practical methods of searching for collections of points that maximize it. Motivation I've come across ...
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1answer
84 views

Maximize with matrices

How do I use maximise with an arbitrary sized symbolic matrix? e.g for a small matrix it is fine to write it out, ...
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2answers
287 views

List of critical points

In TI-Nspire CX CAS, writing: exp▶list(fMax(sin(x),x,0,10),x) I get: {((π)/(2)),((5*π)/(2))} while in Wolfram Mathematica, writing: ...
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2answers
222 views

Problem with Solve (Lagrange multiplier)

I'm trying to solve a simple maximization problem, which I can easily solve by hand using the Lagrangian method. I want to maximize UH subject to ...
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3answers
144 views

How to extract maximum value coordinates from ParametricPlot of function

I have a ParametricPlot ParametricPlot[{Sin[x], 2 Cos[x]}, {x, 0, 2 π}] How to know the maximum value on Y-axix and X-axis?
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Trouble Plotting the maximum values of a function

First off, I apologize if this question is either incredibly obvious, or has been clearly asked and answered before. I've been searching the forum for a while, and the questions and answers thusfar ...
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2answers
57 views

Hot to single out numeric values from NMaximize

I have some problem with NMaximize. The function NMaximize gives result like this NMaximize[f[x],x] {f[xmax] ,{x -> xmax}} I've read in various answers that ...
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2answers
57 views

Finding maximum in the boundary limits using mathematica [closed]

Im trying to find the maximum of the function on the boundary: f[x_, y_] := 10 Log[x^2 + 2 y^2 + 1] - x^2 - y^2 That is within the boundary: ...
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1answer
67 views

Getting the index of maximum while generating the values with table

Say I am tabling the values of a two variable function using a list of indexes (which I can't assume to be ordered), I'd like to return the index (or the list of indexes) which yield the maximum value(...
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1answer
203 views

Finding peaks/maxima while extracting the range of x-values

I have read similar questions about finding peaks on the web (Finding peaks of data) as well as the FindPeaks function but I'm struggling to put them into proper context for my case. I am still a new ...
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3answers
194 views

Maximization of a function over a discrete set

I have a function of three variables: $f = f(x, y, z)$. I need to maximize $f$, when $x$, $y$ and $z$ run given sets of values: $x \in (x_1, x_2, x_3)$, $y \in (y_1, y_2, y_3)$ and $z \in (z_1, z_2, ...
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1answer
61 views
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90 views

How to maximize the modulus of a multivariate complex-valued function?

My problem is the following. I have a messy, complex-valued function ...
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1answer
71 views

Has Mathematica derived the maximum here?

Suppose I define a function as f[l_, a_, p_] := (l^(1 - 2*p))/(l + a) Then I solve the expression for the first derivative equalling to zero for ...