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Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
1
vote
How to extract the last output from the Maximize
All of the answers in @kglr's comment work:
nm = Maximize[{x^0.5 - 2*y^3, 0 < x < 1, 0 < y < 1}, {x, y}];
y /. Last[nm]
y /. nm[[-1]]
nm[[-1, -1, -1]]
(* 0.000023912 *)
(* 0.000023912 *)
(* 0.0000239 …
2
votes
Accepted
Solving for the coefficients in a nonlinear equation according to constraints
This can be solved by choosing a few arbitrary values of θ:
FullSimplify[
Solve[0 == E^t (a x^2 + b y^2 + c z^2)
/. {x -> r Cos[θ], y -> r Sin[θ], z -> m} /. θ -> {0, 1, 2}, {a, b}]]
(* {{a -> …
12
votes
1
answer
365
views
Bug in NMaximize in 12.2?
Bug introduced in 12.2, Fixed in 12.3
Something changed in NMaximze in v12.2:
NMaximize[E^(-x^2) - 1, x]
(* {(-1 + E^#1)[0.], {x -> 0.}} *)
v12.1 works as expected:
NMaximize[E^(-x^2) - 1, x]
(* {0., …
8
votes
FindMinimum works only if you know the answer
This is more of an extended comment than an answer. First, building off @JackLaVigne's work, I think it's better to work in log of your parameters, so I defined a new objective function
chiSquared2[ …
4
votes
Accepted
Plotting maxima within a simplex
Piggybacking on @kglr's answer, but using a right triangle rather than equilateral, so we can see p and q on the axes and to highlight the symmetry between f and h.
How about:
Plot3D[max[p, q], {p, …
6
votes
4
answers
712
views
MaxDetect speed
What's the fastest way to find the local maxima of a 2D list? E.g.
nx = ny = 100;
dat = Table[Sin[2. \[Pi] x/nx] (0.1 + Cos[2. \[Pi] y/ny]), {y, 0, ny}, {x, 0, nx}];
ListPlot3D[dat]
This (updat …
1
vote
Solve / brute-force for parameters that drive a function to zero at specified points
I have no idea on your actual problem, but your simple example can be solved by choosing a few arbitrary values of θ:
FullSimplify[
Solve[0 == E^t (a x^2 + b y^2 + c z^2)
/. {x -> r Cos[θ], y - …
6
votes
Accepted
Colouring Bifurcation Diagram
You can use ContourPlot to make such 1D bifurcation diagrams easily as in this answer, using ConditionalExpression to handle the stability analysis. I assume g[x, r] is some kind of potential, not x' …