Questions tagged [constraint]
The constraint tag has no usage guidance.
127
questions
0
votes
1answer
48 views
Maximization under constraints / find maxima
I am trying to code the following maximization program that I am not able to solve algebraically (Of course I manage to get the first derivative, but struggle finding its root):
$\begin{equation} Max_{...
1
vote
0answers
31 views
Find the ratio of two volumes of 6 x 6 positive-definite symmetric matrices
Consider the class $A$ of $6 \times 6$ positive definite matrices with real entries and unit trace (that is, the sum of the six diagonal entries is 1). (In quantum information-theoretic parlance, this ...
1
vote
1answer
53 views
Control evaluation for functional constraints
I'm trying to understand how to use Mathematica to find a solution subject to constraints, where one of the constraints is specified as a predicate function. But I don't know how to control evaluation ...
-1
votes
0answers
26 views
Approximating polynomial under monotonicity constraint [migrated]
Given a bivariate data set, how does one obtain the most accurate least-squares polynomial approximation under the constraint that the resulting polynomial is non-decreasing. Similarly, how does one ...
0
votes
0answers
52 views
Construction of Navigation Function: Error
https://en.wikipedia.org/wiki/Navigation_function
https://www.sciencedirect.com/science/article/abs/pii/S0921889015302451
https://arxiv.org/pdf/1605.00638.pdf - Paragraph III
I am trying to create a ...
0
votes
2answers
101 views
listing of vectors satisfying some special constraint
We have
list = {{1, 1, 0}, {1, 0, 1}, {0, 1, 1}, {-1, 1, 0}, {1,-1, 0}, {-1, -1, 0}, {-1, 0, 1}, {1, 0, -1},{-1, 0, -1},{0, -1, 1},{0, 1, -1},{0, -1, -1}}
...
2
votes
2answers
109 views
FindMinimum with constraint produces incorrect results
Issuing the following:
FindMinimum[{x, ((2 x + 1)/(3 x - 2))^(4 x - 3) <= 10^-10}, {x, 2}]
produces a value of 13.1686 . The constraint for that value is: 1....
1
vote
3answers
122 views
Maximize - Non binding constraint is changing the result
When I add a non-binding constraint to a maximization problem the result changes. I don't understand why.
Below you can find the code that I am using.
For the maximization A, H = 6837.66
For the ...
2
votes
1answer
43 views
In NMinimize, how to incorporate constraints on positive semidefiniteness of a matrix which is not the matrix variable being optimised?
The problem
I want to solve the following problem for symmetric matrix $X$:
$$
\begin{aligned}
\min_{X\succ 0} \; & -\log(\det(X)) & \\ \text{subject to} \; & \begin{pmatrix} X &...
2
votes
2answers
59 views
Calculate the Viswanath's constant (Random Fibonacci sequences)
How Can I calculate first few digits of Viswanath's constant?
Viswanath’s constant ≈ 1.1319882487943 is a real number whose nth power approximates the absolute value of the nth term of some random ...
0
votes
0answers
37 views
Constraints and Tolerance
So I'm running NMaximize for optimizing a value and for constraints, I need the parameters to belong to a discrete set of elements. Basically, the constraint looks ...
0
votes
1answer
61 views
How to find a numerical solution for a differential equation with constraints?
I want first to apologize for my poor english level ^^ Let me present my issue.
I want resolve numerically (I use Python) for x in [0;1] the following differential equation : $$dy/dx = a(y - y^2) $$
...
2
votes
1answer
104 views
Verify a conjectured formula for a modification of a 3D constrained integration successfully solved using Mathematica
I've acquired somewhat indirect--and not fully conclusive--evidence that the solution of a certain three-dimensional constrained integration takes the form
...
1
vote
1answer
28 views
Plotting 3D region depending on 2 parameters with constraints
I'm trying to plot the full range that a set of estimates gives. They depend on some parameters and conditions, but I haven't been able to to it effectively with RegionPlot3D. Here is the set that I ...
0
votes
0answers
35 views
Bug with ValueQ involving fractions? [duplicate]
Expected behavior:
ClearAll[f];
ValueQ[f[1]]
False
Unexpected behavior:
...
0
votes
1answer
93 views
Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure
Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint
...
2
votes
1answer
87 views
Solving an equation with a constraint involving not-equal
I am trying to solve an equation with a constraint involving not-equal.
For example:
$2 x + 3 y = 5$ with the constraint $2 x + 4 ≠ 2$.
How should I approach this?
Edit 1
I tried the suggestions in ...
1
vote
2answers
174 views
Confirm and possibly simplify a 2009 result for a 2D constrained integration
This is a direct descendant of two other recent questions,
3D and Equivalence,
both of which have been
answered in skillful, interesting manners. (See also the comment [actually answer] of JimB to
...
1
vote
1answer
55 views
How to force LinearModelFit to return Non-negative coefficients?
LinearModelFit[{m,v}] will return a coefficients list $\beta$ from the design matrix $m$ and response vector $v$, where $m.\beta$ is fitted to $v$. However, the ...
0
votes
2answers
48 views
FindMaximum under binary constrains
I'm trying to find a maximum for a function whose variables have binary values (either -1 or 1). The clumsy code for that constraint I use is shown below. There must be a more compact code, and I ...
2
votes
3answers
358 views
Evaluate a certain three-dimensional constrained integral
The result of the three-dimensional integration
...
0
votes
0answers
38 views
Maximization by imposing an asymptote constraint
I am trying to plot the profit curve for optimal e(or effort)
with respect to c.
...
3
votes
0answers
58 views
How to generate a large number of constraints for all indices ($\forall i$)
Is it possible to generate a set of constraints in the form "$\forall$".
For example:
\begin{align}
\min\ & f\left(\sum x_i\right)\\
s.t.\ & \\
& x_i\geq 17 && \forall i=...
2
votes
1answer
126 views
Solving symbolic system of non-linear equations takes too long
I am trying to solve a set of system of symbolic non-linear equations:
...
4
votes
1answer
58 views
Nonlinearmodelfit with integral or nintegral as constrain
Until now I have been using the Nonlinearmodelfit without any issues, but I want to add a new constrain (Integral or NIntegral) to my modelfit.
My fitting function is ...
0
votes
1answer
97 views
Global optimisation - Error bound on NMaximize?
Is it possible to obtain an error bound on NMaximize? e.g. convert the number returned by NMaximize into a rigorous upper bound ...
1
vote
0answers
40 views
Tackling variational problem with constraints [closed]
I need to minimize (preferably symbolically) functional with constraints:
$$
F = \int_{0}^{\pi/2} f(x)cos{x}dx\,\\
1.1 \geq f(x) \geq 0\\
2.\int_{0}^{\pi/2} f(x)dx=Const\\
3. f(0) =1\\
4.f(\pi/2) = 0\...
0
votes
1answer
52 views
1
vote
1answer
93 views
Constrained NDSolve
Consider n particles constrained on the surface of a unit sphere. $i^{th}$ particle experiences a force from every other $j^{th}$ of the form $$\vec{f_{ij}}=\frac{k ...
5
votes
1answer
121 views
How do I tell FindMinimum to only work with positive, real numbers?
I have a function that I'm trying to minimize. It currently works reasonably well with this:
...
0
votes
0answers
38 views
Maximising the minimum of a linear combination of polynomials
I have list of finArray of 6 rational polynomials, of degrees of about 4 to 6, in around 200 variables allVars, along with a ...
0
votes
2answers
90 views
Is it possible to use Reduce in a way that “eliminates” some unwanted variables, and only gives constraints between wanted variables?
Reduce[{x == z, y == z}] gives y == z && x == z but say I'm only interested in constraints that appear between ...
0
votes
1answer
40 views
Find parameter value for which sharply-peaked constrained 3d-integral equals 1
I want to find the value (desirably to high-precision) of the parameter $i$ for which
the constrained 3d integration
...
0
votes
0answers
37 views
What happens when NMinimize constraints are unsolvable
I have an algebraic function in many variables which outputs a vector $v$.
The coefficients of the vector are high degree polynomials in many variables.
I want to maximize $\;v[[1]] /Norm[v]\;$ ...
1
vote
1answer
81 views
Finding whether the convex cone from a vector list is null
Given a list of vectors, I want to find whether there exists a vector such that its dot product with those in the list is all (semi)positive, or at least above a certain small negative value.
5
votes
3answers
211 views
How to randomly generate a positive semidefinite matrix?
How would I randomly generate a positive semidefinite matrix? I'm aware how to generate a random $n\times n$ matrix with real values between -1 and 1 with
...
1
vote
1answer
43 views
Show, if possible, small isolated “islands” in the unit cube using RegionPlot3D
I have a certain three-dimensional constraint
...
1
vote
1answer
137 views
ArgMin over intervals and discrete sets
I was playing with ArgMin but I'm not sure how to use it for constrained optimization.
For example,
ArgMin[x^2, x]
returns <...
1
vote
2answers
50 views
Find maximum of x given a bunch of constraints [closed]
Trying to find maximum of x given that '''0<=x<=3''' and some other stuff. This works fine:
Clear[x, y]
FindMaximum[{x, 0<=x<=3}, x]
But this does ...
3
votes
3answers
179 views
Constraint of NDSolve with an integral of the solution
I'd like to use NDSolve and to make a constraint with an integral.
For example, take the very simple : $$f'(x)=-f(x)/x_0 $$
the solution is $$f(x)=f_0 e^{-x/x_0} $$
And $f_0$ is given by : $$\int_0^{+\...
1
vote
2answers
109 views
Optimize with constraints
I want to find the smallest $k$ such that $kx^2 \ge (\sin(x)-x)^2$ for all scalar $x\in[a,\ b]$? Obviously, I can do it analytically, but how can I do it (symbolically) in Mathematica? I am new to ...
0
votes
1answer
136 views
0
votes
1answer
66 views
NonlinearModelFit failing because varible range [closed]
I'm trying to fit a specific equation to a plot of points but its failing because the equation has a square root in it and I need to keep the values of x between a certain range. I know how to do this ...
4
votes
3answers
508 views
How to set a tolerance level for equality constraints
Given two equality constraints: x+y==250 and z+p==65 where x=190, y=50, z=45, p=15, I want ...
1
vote
1answer
42 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 ...
5
votes
3answers
282 views
12
votes
0answers
208 views
Linear programming with lazy constraints
Does Mathematica offer any means for solving linear programming problems with "lazy constraints", as described e.g. here?
While I am not very familiar with linear programming, my understanding of the ...
3
votes
1answer
171 views
Solving a stiff nonlinear ODE system
The system I am trying to solve is simple, but looks pretty stiff and I have unsuccessfully tried to solve it with StiffnessSwitching. It is the following one:
<...
1
vote
1answer
35 views
Numerical Maximization with Alternating Sum
I need to maximize a function that involves an alternating sum and a set of constraints. I have tried the following code:
NMaximize[{(-1)^{m}*n!, n + m == 7, m > 0, n > 0}, {m, n}]
However, the ...
6
votes
4answers
873 views
RandomInteger with equal number of 1 and -1
I want to generate a list of random integers with only three values 1,0,-1. I know it can be done through RandomInteger[{-1, 1}, n]. How can I impose constraint on this list so that every integers in ...
