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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1answer
45 views

How to maximize an expression within an interval? [closed]

I have tried to maximize this expression but in the interval -1<= x <=1 , but I can't get the correct syntax ...
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1answer
59 views

Maximize an expression with respect to a variable after its minimization with respect to other variables

I started to use Mathematica a few time ago. I want to minimize the following expression (function of $l,p,q,r,c$) with respect to variables $l, p, q, r$ and then maximize the result obtained with ...
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1answer
32 views

Minimize a function of a variable of four variables and one parameter with constraints

I just started to use Mathematica. Using the following simple command to minimize a function of variables $a,b,c,d$ with parameter $n$, it takes too much time. Do you know if there is a mistake in ...
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3answers
66 views

How to find maxima of a numerical calculation

Suppose I have the following code: ...
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53 views

NMinimize: How to avoid solutions that do not satisfy constraints within a certain tolerance?

I just started to use Mathematica a few weeks ago. Using NMinimze, I would like to avoid solutions that do not satisfy certain constraints (although they "almost" satisfy them). Do you know ...
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0answers
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Maximize taking too long

I just started to use Mathematica a few weeks ago. I am afraid there is something that does not work on my laptop because, for the following simple command, it takes too much time. Do you know if ...
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2answers
120 views

Finding the maximum of a piecewise function

I have the following piecewise function of the variable $e_f$: $$g(a,b,c,w,F,e_h,e_f)=\begin{cases} \frac{(c-a e_f) (e_f (4e_f w-a)+c)}{8 b e_f^2} & \left(e_f=e_h\land e_f>\frac{c}{a}\...
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1answer
39 views

Problems in optimizing a function over two variables

The following function needs to be maximized over the variable $a1$ and $a2$ in the range $0 \le a1 <1$ and $0\le a2 <1$: ...
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2answers
73 views

How to find the maximum of this using Nmaximise?

I have a function ...
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0answers
51 views
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1answer
26 views

How to find the local maximum and minium points,as well as the interval of increase/decrease on the derivative equation [closed]

How to find the local maximum and minimum points, as well as the interval of increase/decrease on the derivative equation,x^6-10x^5-780^3+2500x^2
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35 views

Problem with NMaximize and intervals

My expression is ...
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2answers
27 views

How to find $ (x, y) $ corresponding to $ z_\text{max} $ in $ \{x, y, z\} $-table?

I have been given a table a of the form ...
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1answer
85 views

How do I find the maximum of this quantity?

I am looking for the maximum of the function $$V(r^*)=\left( 1-\dfrac{2m}{r} \right)\left( \dfrac{l(l+1)}{r^2}-\dfrac{6m}{r^3} \right)$$ in the coordinate $r^*$ for given $l$ and $m$, where $r^*=r+...
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1answer
43 views

Nested maximum function not working

I am trying to maximize a function which is itself a maximized function. For example, see the below. Can someone explain this error: ...
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1answer
53 views

How to plot and print the maximum value in a ContourListPlot[]

I have managed to manipulate functions from a list of data points. The data table is large and thus is in this link. ...
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2answers
50 views

Maximise a function over real and complex parameters [closed]

I have the function f[b_x_] := Exp[-I b] Sin[I x], where $x$ is real and $b$ is complex. I want to maximise the function $f$ over $x$ and $b$, but it is ...
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1answer
50 views

Position of maximum element in list under optimisation

For a list of several functions: functions = {a[x,y,z],b[x,y,z],c[x,y,z],d[x,y,z]}; I want to maximize the maximum value of a function of three variables. This ...
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1answer
38 views

Maximise over functions in Mathematica

Define the functions $h$, $j$, and $k$ that are each functions of 3 variables: h[x,y,z] j[x,y,z] k[x,y,z] How can I find the max of these functions? I want the ...
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1answer
56 views

How to find the distances between two adjacent maxima in a solution from NDSolve

I try to find a general approach to plot the time evolution of horizontal distances from maximum to maximum in a solution of PDE. The solution u[x,t] normally have ...
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1answer
63 views

Why can MaxValue simply not get the exact result I want? [closed]

8/7 (9 + 4 Sqrt[2]) That's the result I want. How can I get x and y at the same time with respect to max? How can I add the constraint that both x and y belong to ...
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0answers
57 views

FindMaximum error (not a real number)

For the code below, I get several error messages once I click the "Enable Dynamics" button. However, once I run the code, the output works fine, so, if that is all I wished to do, I would just live ...
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0answers
28 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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1answer
39 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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1answer
61 views
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62 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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2answers
75 views

problem with maximize function and envelope function

I Have the problem with the maximize of this problem: ...
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2answers
86 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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0answers
21 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
55 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
62 views

Maximization of a a PiecewiseExpand funcion

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

Optimising the Selection of MaxValue in Association

Suppose I have the following Association: ...
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4answers
94 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
73 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
54 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
56 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
104 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
100 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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2answers
385 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
73 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
107 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
63 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
111 views

Plot maximum value of a function of three variables

Given a function f[\[Theta]_, \[Phi]_, t_] given by ...
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1answer
73 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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2answers
47 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
307 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
113 views

Problem with constraints of NMaximize

I am using NMaximize to solve the following problem. ...
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1answer
62 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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0answers
81 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
51 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 ...