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NMaximize is not converging to a solution
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NMaximize is not converging to a solution
Declaration of variables in large Linear Programming model with NMaximizeHow trustworthy is NMaximize?Numeric range: present or notMaximalBy[#, “votes”] & not equal to MaximalBy[“votes”]?Maximimize not working properly?Does fitting data get stuck by non-homogeneous interval of data?How to find maximum (not with numbers,but with parameters) of 2-variables function under constraints?Hot to single out numeric values from NMaximizeNSum: Summand (or its derivative) is not numerical at pointProblem with constraints of NMaximize
$begingroup$
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 the function.
I can see the constraints are such that the value is bounded but I get the below warning messages:
NMaximize::cvmit: Failed to converge to the requested accuracy or
precision within 100000 iterations.
NMaximize::cvdiv: Failed to
converge to a solution. The function may be unbounded.
The constraint and the way I am using the function is as below:
constraint = (x | y) [Element]
Integers && ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x -
3.63201*10^84 x^2]) || (10713. <= x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2]))
maxX =
NMaximize[{x, constraint}, {x, y}, MaxIterations -> 100000]
I have increased the MaxIterations from 100 to 100000 but it doesn't seem to converge. I am not sure if increasing the MaxIterations is the solution. Can you please guide me with this?
functions maximum
asked 1 hour ago
gagansogaganso
1407
$endgroup$
|
show 1 more comment
$begingroup$
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 the function.
I can see the constraints are such that the value is bounded but I get the below warning messages:
NMaximize::cvmit: Failed to converge to the requested accuracy or
precision within 100000 iterations.
NMaximize::cvdiv: Failed to
converge to a solution. The function may be unbounded.
The constraint and the way I am using the function is as below:
constraint = (x | y) [Element]
Integers && ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x -
3.63201*10^84 x^2]) || (10713. <= x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2]))
maxX =
NMaximize[{x, constraint}, {x, y}, MaxIterations -> 100000]
I have increased the MaxIterations from 100 to 100000 but it doesn't seem to converge. I am not sure if increasing the MaxIterations is the solution. Can you please guide me with this?
functions maximum
asked 1 hour ago
gagansogaganso
1407
$endgroup$
$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
1
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?constraint /. x -> 19762results iny [Element] Integers && 7229.16 < y < 7344.29andconstraint /. x -> 19763results inFalse.
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB, I think forx,yisn't needed. Thanks for pointing this out. But if I am trying to maximizey, I need to maximize over both the variables sinceyis an expression ofx, right?
$endgroup$
– gaganso
1 hour ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago
|
show 1 more comment
$begingroup$
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 the function.
I can see the constraints are such that the value is bounded but I get the below warning messages:
NMaximize::cvmit: Failed to converge to the requested accuracy or
precision within 100000 iterations.
NMaximize::cvdiv: Failed to
converge to a solution. The function may be unbounded.
The constraint and the way I am using the function is as below:
constraint = (x | y) [Element]
Integers && ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x -
3.63201*10^84 x^2]) || (10713. <= x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2]))
maxX =
NMaximize[{x, constraint}, {x, y}, MaxIterations -> 100000]
I have increased the MaxIterations from 100 to 100000 but it doesn't seem to converge. I am not sure if increasing the MaxIterations is the solution. Can you please guide me with this?
functions maximum
asked 1 hour ago
gagansogaganso
1407
$endgroup$
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 the function.
I can see the constraints are such that the value is bounded but I get the below warning messages:
NMaximize::cvmit: Failed to converge to the requested accuracy or
precision within 100000 iterations.
NMaximize::cvdiv: Failed to
converge to a solution. The function may be unbounded.
The constraint and the way I am using the function is as below:
constraint = (x | y) [Element]
Integers && ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x -
3.63201*10^84 x^2]) || (10713. <= x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-43 Sqrt[
4.98614*10^92 + 4.65469*10^88 x - 3.63201*10^84 x^2]))
maxX =
NMaximize[{x, constraint}, {x, y}, MaxIterations -> 100000]
I have increased the MaxIterations from 100 to 100000 but it doesn't seem to converge. I am not sure if increasing the MaxIterations is the solution. Can you please guide me with this?
functions maximum
functions maximum
asked 1 hour ago
gagansogaganso
1407
asked 1 hour ago
gagansogaganso
1407
asked 1 hour ago
gagansogaganso
1407
asked 1 hour ago
gagansogaganso
1407
asked 1 hour ago
gagansogaganso
1407
1407
$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
1
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?constraint /. x -> 19762results iny [Element] Integers && 7229.16 < y < 7344.29andconstraint /. x -> 19763results inFalse.
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB, I think forx,yisn't needed. Thanks for pointing this out. But if I am trying to maximizey, I need to maximize over both the variables sinceyis an expression ofx, right?
$endgroup$
– gaganso
1 hour ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago
|
show 1 more comment
$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
1
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?constraint /. x -> 19762results iny [Element] Integers && 7229.16 < y < 7344.29andconstraint /. x -> 19763results inFalse.
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB, I think forx,yisn't needed. Thanks for pointing this out. But if I am trying to maximizey, I need to maximize over both the variables sinceyis an expression ofx, right?
$endgroup$
– gaganso
1 hour ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago
$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
1
1
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?
constraint /. x -> 19762 results in y [Element] Integers && 7229.16 < y < 7344.29 and constraint /. x -> 19763 results in False.$endgroup$
– JimB
1 hour ago
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?
constraint /. x -> 19762 results in y [Element] Integers && 7229.16 < y < 7344.29 and constraint /. x -> 19763 results in False.$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB, I think for
x, y isn't needed. Thanks for pointing this out. But if I am trying to maximize y, I need to maximize over both the variables since y is an expression of x, right?$endgroup$
– gaganso
1 hour ago
$begingroup$
@JimB, I think for
x, y isn't needed. Thanks for pointing this out. But if I am trying to maximize y, I need to maximize over both the variables since y is an expression of x, right?$endgroup$
– gaganso
1 hour ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
Rationalize the constraint:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y < 2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <= x <=
19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) //
Rationalize[#, 0] & // Simplify;
With the Rationalized constraint you can use Maximize:
maxX = Maximize[{x, constraint2}, {x, y}]
(* {19762, {x -> 19762, y -> 7287}} *)
constraint2 /. maxX[[2]]
(* True *)
EDIT: To find maximum y
(maxY = Maximize[{y, constraint2}, {x, y}]) // N
To plot the region defined by the constraint:
reg = ImplicitRegion[constraint2, {x, y}];
Region[reg,
Frame -> True,
FrameLabel -> (Style[#, 12, Bold] & /@ {x, y}),
Epilog -> {Red,
AbsolutePointSize[3],
Point[{x, y} /. maxX[[2]]],
Point[{x, y} /. maxY[[2]]]}]
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
$endgroup$
add a comment |
$begingroup$
You have numbers spread a wide range of magnitudes for no good reason. This range is probably too wide for machine precision arithmetic. Also telling NMinimize explicitly that this an integer optimization problem seems to help. Try this:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <=
x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) // Expand
maxX = NMaximize[{x, constraint2}, {x, y}, Integers,
MaxIterations -> 10000]
{19762., {x -> 19762, y -> 7311}}
And with your definition of constraint:
constraint /. maxX[[2]]
True
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
$endgroup$
$begingroup$
Butconstraint /. x -> 19762 /. y -> 8647results inFalse?
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works forxbut when I try to find the maximumysimilarly, I still get the same message -NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.
$endgroup$
– gaganso
1 hour ago
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Rationalize the constraint:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y < 2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <= x <=
19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) //
Rationalize[#, 0] & // Simplify;
With the Rationalized constraint you can use Maximize:
maxX = Maximize[{x, constraint2}, {x, y}]
(* {19762, {x -> 19762, y -> 7287}} *)
constraint2 /. maxX[[2]]
(* True *)
EDIT: To find maximum y
(maxY = Maximize[{y, constraint2}, {x, y}]) // N
To plot the region defined by the constraint:
reg = ImplicitRegion[constraint2, {x, y}];
Region[reg,
Frame -> True,
FrameLabel -> (Style[#, 12, Bold] & /@ {x, y}),
Epilog -> {Red,
AbsolutePointSize[3],
Point[{x, y} /. maxX[[2]]],
Point[{x, y} /. maxY[[2]]]}]
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
$endgroup$
add a comment |
$begingroup$
Rationalize the constraint:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y < 2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <= x <=
19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) //
Rationalize[#, 0] & // Simplify;
With the Rationalized constraint you can use Maximize:
maxX = Maximize[{x, constraint2}, {x, y}]
(* {19762, {x -> 19762, y -> 7287}} *)
constraint2 /. maxX[[2]]
(* True *)
EDIT: To find maximum y
(maxY = Maximize[{y, constraint2}, {x, y}]) // N
To plot the region defined by the constraint:
reg = ImplicitRegion[constraint2, {x, y}];
Region[reg,
Frame -> True,
FrameLabel -> (Style[#, 12, Bold] & /@ {x, y}),
Epilog -> {Red,
AbsolutePointSize[3],
Point[{x, y} /. maxX[[2]]],
Point[{x, y} /. maxY[[2]]]}]
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
$endgroup$
add a comment |
$begingroup$
Rationalize the constraint:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y < 2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <= x <=
19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) //
Rationalize[#, 0] & // Simplify;
With the Rationalized constraint you can use Maximize:
maxX = Maximize[{x, constraint2}, {x, y}]
(* {19762, {x -> 19762, y -> 7287}} *)
constraint2 /. maxX[[2]]
(* True *)
EDIT: To find maximum y
(maxY = Maximize[{y, constraint2}, {x, y}]) // N
To plot the region defined by the constraint:
reg = ImplicitRegion[constraint2, {x, y}];
Region[reg,
Frame -> True,
FrameLabel -> (Style[#, 12, Bold] & /@ {x, y}),
Epilog -> {Red,
AbsolutePointSize[3],
Point[{x, y} /. maxX[[2]]],
Point[{x, y} /. maxY[[2]]]}]
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
$endgroup$
Rationalize the constraint:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y < 2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <= x <=
19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) //
Rationalize[#, 0] & // Simplify;
With the Rationalized constraint you can use Maximize:
maxX = Maximize[{x, constraint2}, {x, y}]
(* {19762, {x -> 19762, y -> 7287}} *)
constraint2 /. maxX[[2]]
(* True *)
EDIT: To find maximum y
(maxY = Maximize[{y, constraint2}, {x, y}]) // N
To plot the region defined by the constraint:
reg = ImplicitRegion[constraint2, {x, y}];
Region[reg,
Frame -> True,
FrameLabel -> (Style[#, 12, Bold] & /@ {x, y}),
Epilog -> {Red,
AbsolutePointSize[3],
Point[{x, y} /. maxX[[2]]],
Point[{x, y} /. maxY[[2]]]}]
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
edited 48 secs ago
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
answered 24 mins ago
Bob HanlonBob Hanlon
61.4k33598
61.4k33598
add a comment |
add a comment |
$begingroup$
You have numbers spread a wide range of magnitudes for no good reason. This range is probably too wide for machine precision arithmetic. Also telling NMinimize explicitly that this an integer optimization problem seems to help. Try this:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <=
x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) // Expand
maxX = NMaximize[{x, constraint2}, {x, y}, Integers,
MaxIterations -> 10000]
{19762., {x -> 19762, y -> 7311}}
And with your definition of constraint:
constraint /. maxX[[2]]
True
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
$endgroup$
$begingroup$
Butconstraint /. x -> 19762 /. y -> 8647results inFalse?
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works forxbut when I try to find the maximumysimilarly, I still get the same message -NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.
$endgroup$
– gaganso
1 hour ago
add a comment |
$begingroup$
You have numbers spread a wide range of magnitudes for no good reason. This range is probably too wide for machine precision arithmetic. Also telling NMinimize explicitly that this an integer optimization problem seems to help. Try this:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <=
x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) // Expand
maxX = NMaximize[{x, constraint2}, {x, y}, Integers,
MaxIterations -> 10000]
{19762., {x -> 19762, y -> 7311}}
And with your definition of constraint:
constraint /. maxX[[2]]
True
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
$endgroup$
$begingroup$
Butconstraint /. x -> 19762 /. y -> 8647results inFalse?
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works forxbut when I try to find the maximumysimilarly, I still get the same message -NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.
$endgroup$
– gaganso
1 hour ago
add a comment |
$begingroup$
You have numbers spread a wide range of magnitudes for no good reason. This range is probably too wide for machine precision arithmetic. Also telling NMinimize explicitly that this an integer optimization problem seems to help. Try this:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <=
x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) // Expand
maxX = NMaximize[{x, constraint2}, {x, y}, Integers,
MaxIterations -> 10000]
{19762., {x -> 19762, y -> 7311}}
And with your definition of constraint:
constraint /. maxX[[2]]
True
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
$endgroup$
You have numbers spread a wide range of magnitudes for no good reason. This range is probably too wide for machine precision arithmetic. Also telling NMinimize explicitly that this an integer optimization problem seems to help. Try this:
constraint2 = ((x == 0 && 1. <= y <= 12720.) || (1. <= x <= 10712. &&
0 <= y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2]) || (10713. <=
x <= 19762. &&
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) -
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2] < y <
2.08565*10^-36 (3.04959*10^39 + 2.24751*10^34 x) +
2.8484*10^-1 Sqrt[
4.98614*10^8 + 4.65469*10^4 x - 3.63201 x^2])) // Expand
maxX = NMaximize[{x, constraint2}, {x, y}, Integers,
MaxIterations -> 10000]
{19762., {x -> 19762, y -> 7311}}
And with your definition of constraint:
constraint /. maxX[[2]]
True
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
edited 1 hour ago
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
answered 1 hour ago
Henrik SchumacherHenrik Schumacher
59.3k582165
59.3k582165
$begingroup$
Butconstraint /. x -> 19762 /. y -> 8647results inFalse?
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works forxbut when I try to find the maximumysimilarly, I still get the same message -NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.
$endgroup$
– gaganso
1 hour ago
add a comment |
$begingroup$
Butconstraint /. x -> 19762 /. y -> 8647results inFalse?
$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works forxbut when I try to find the maximumysimilarly, I still get the same message -NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.
$endgroup$
– gaganso
1 hour ago
$begingroup$
But
constraint /. x -> 19762 /. y -> 8647 results in False?$endgroup$
– JimB
1 hour ago
$begingroup$
But
constraint /. x -> 19762 /. y -> 8647 results in False?$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@JimB D'oh. Yeah, I did the simplification wrong. -.- Thanks for pointing that out.
$endgroup$
– Henrik Schumacher
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works for
x but when I try to find the maximum y similarly, I still get the same message - NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.$endgroup$
– gaganso
1 hour ago
$begingroup$
@HenrikSchumacher, thank you for this. This works for
x but when I try to find the maximum y similarly, I still get the same message - NMaximize[{y, res}, {x, y}, Integers, MaxIterations -> 100000]. Output: NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.$endgroup$
– gaganso
1 hour ago
add a comment |
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$begingroup$
Could try maximizing over individual regions of the piecewise set-up. But the machine precision values will make validation of inequalities kind of iffy.
$endgroup$
– Daniel Lichtblau
1 hour ago
1
$begingroup$
I'm not seeing what $y$ has to do with this. Wouldn't the maximum value of $x$ be 19762?
constraint /. x -> 19762results iny [Element] Integers && 7229.16 < y < 7344.29andconstraint /. x -> 19763results inFalse.$endgroup$
– JimB
1 hour ago
$begingroup$
@JimB, I think for
x,yisn't needed. Thanks for pointing this out. But if I am trying to maximizey, I need to maximize over both the variables sinceyis an expression ofx, right?$endgroup$
– gaganso
1 hour ago
$begingroup$
Yes, if that's what you want. The general solution appears to be $x = 19762$ and $7230leq y leq 7344$. So to maximize $y$ you'd choose $7344$.
$endgroup$
– JimB
29 mins ago
$begingroup$
@JimB, thank you. But I think the value of $y$ can be greater than 7344 for different values of $x$. For example, at $x = 7504$, the maximum value of y is 13937.
$endgroup$
– gaganso
25 mins ago