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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: ...
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 ...
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 ...
52 views

Reduce, Piecewise function gives result that does not make any sense given condition constraint

Here is my code: ...
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:...
69 views

problem with maximize function and envelope function

I Have the problem with the maximize of this problem: ...
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 ...
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 ...
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]) ...
51 views

Maximization of a a PiecewiseExpand funcion

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

Optimising the Selection of MaxValue in Association

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

Sorting polynomials based on their y value and finding their intersection

I've got the following list of polynomials, ...
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 ...
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 ...
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 ...
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 $s_2$....
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 ...
372 views

How can I get exact maximal value of this expression?

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

Plot maximum value of a function of three variables

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

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 ...
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 ...
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 ...
133 views

Finding a maximum on a plot

My script is currently: ...
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 ...
131 views

Periodogram local maximum

I want to find dominant frequencies of periodogram exactly. ...
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 ...
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, ...
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: ...
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 ...
74 views

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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?
35 views

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 ...
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 ...
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: ...
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(...
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 ...
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, ...
61 views

How to find maximum (not with numbers,but with parameters) of 2-variables function under constraints?

I have these functions: ...