Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
1,329
questions
3
votes
1answer
547 views
Handing a list of constraint expressions to a C++ function with MathLink
I need to solve an optimization problem, which is defined in a Mathematica notebook.
Using Mathematica's FindMinimum is not an option, because it is too slow. So, ...
40
votes
3answers
4k views
Identifying critical points/lines of 2/3D image/cubes
Upshot
I am interested in identifying critical points of a 3D field/cubes (maxima, minima, tube-like and wall-like saddle points) and 2D field/image (maxima, minima, saddle points). I.e. the ...
12
votes
4answers
485 views
How can I efficiently check if a graph is unit distance?
A unit distance graph is a graph that is embeddable in the plane so that every edge has length 1.
...
8
votes
3answers
2k views
How to find the maximum value of an integer that satisfies some inequality
Consider the following Mathematica expression:
Reduce[2^j/(j + 1) <= 10, j, Integers]
which outputs:
...
1
vote
2answers
4k views
Find the dimensions of a cylindrical can that will minimize the cost of the material
A cylindrical can is to be made to hold 1 L of oil. Find the dimensions
that will minimize the cost of the metal to manufacture the can.
This is a standard calculus problem.
The volume of the ...
3
votes
1answer
522 views
parameter optimization
Does anybody know of any tutorial material that explains how to use Mathematica to fit parameter values used in a set of ordinary differential equations to experimental values stored in a comma ...
7
votes
1answer
1k views
Semidefinite Programming
I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
2
votes
0answers
316 views
Having difficulty with the Minimize command
I am having trouble getting an answer to this question...Am I missing something that anybody can see.
...
3
votes
2answers
2k views
optimization problem with NDSolve
I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct:
...
2
votes
1answer
1k views
Optimizing a function involving NDSolve results in error messages
I want to minimize a function f with NMinimize but an error occurs that says:
...
5
votes
2answers
741 views
What alternative notation of subscripts/superscripts that are also treated as SYMBOLS in Mathematica?
I tried to avoid using the subscript $A_0$ in the Module, and get an error with $A[0]$.
...
20
votes
2answers
2k views
Optimization with assumptions
I have the following problem, when I am trying to optimize function with pre-defined assumptions.
I am using Mathematica 8 and I wrote the following simple code
...
4
votes
1answer
1k views
How to solve a quadratic integer programming problem?
I want to solve a quadratic integer programming problem in Mathematica. My first attempt looks like this:
...
6
votes
1answer
350 views
Numerical problems with calculation of function
I have a problem with a calculation which I try to do with Mathematica (8.0.1).
I have the following function which describes a cone (with half opening angle theta)...
4
votes
1answer
299 views
Assumptions seem not to be considered
In the following a,b is a probability distribution, i.e. a+b==1 with ...
70
votes
5answers
22k views
How to find all the local minima/maxima in a range
I want to find :
all local maxima in range
all local minima in range
From those points I can interpolate and combine functions upper and lower boundary. What I am really interested in, is the mean ...
6
votes
1answer
516 views
Defining a non-linear optimization-problem
Consider the following non-linear optimisation problem:
...
88
votes
2answers
7k views
Shaving the last 50 ms off NMinimize
The epilogue:
A paper where the below answer is used was published. The answer below is cited among the references:)
The background:
I have to fit an objective function for ~10 000 datasets in near ...
9
votes
3answers
521 views
Strange domain dependency with Maximize
I'm using Mathematica 8 and strangely enough this code:
Maximize[{x*(1-0.01 x),x>0},x,Integers]
produces the result ...
12
votes
2answers
3k views
Maximizing a function with assumptions
Using
f[s_] := Log[(s/r)^α ((α - 2) n0 r^α + 2 π Pmax ρ r^2)
/((α - 2) n0 s^α + 2 π Pmax ρ s^2)]/s
When I run the following line:
...
13
votes
4answers
6k views
Minimizing a function of many coordinates
I'm trying to obtain a series of points on the unit sphere with a somewhat homogeneous distribution, by minimizing a function depending on distances (I took $\exp(-d)$). My points are represented by ...
7
votes
1answer
3k views
Solve Lagrange multipliers optimization problem
I have two nested solid figure, where $V(a,h,\tau)$ defines the volume and $A(a,h,t)$ defines the surface. The outer solid figure is parametrized in $a_s$,$h_s$ and $t_s$ (they share a common center). ...
24
votes
2answers
1k views
Obtain approximate Hessian using FindMinimum
According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
5
votes
1answer
214 views
Why is this minimization with Boole functions failing?
I am running this command in Mathematica 8.0.4.0:
...
0
votes
1answer
427 views
Symbolic Optimisation
I'm trying to solve symbolically the following optimisation:
$$
\min_{q_uu}\ \Biggl[ q_u q_{uu}\psi B_{uu} + q_u q_{ud}\psi B_{ud} + q_d q_{du}\psi B_{ud} + q_d q_{dd}\psi B_{dd}
$$
$$
+ \...
15
votes
2answers
2k views
Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?
I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
8
votes
1answer
1k views
Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations
The formal problem
The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
14
votes
3answers
2k views
Strategies to avoid LessEqual::nord in NMinimize?
When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
15
votes
1answer
3k views
Combined numerical minimization and maximization
I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following:
...
