Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
42
votes
2answers
2k views
Shaving the last 50 ms off NMinimize
The background:
I have to fit an objective function for ~10 000 datasets in near real time (with near real time being on the order of about 10 seconds). I compile the huge objective function, so that ...
29
votes
7answers
965 views
26
votes
3answers
3k 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 ...
17
votes
0answers
636 views
Identifying critical points 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 ...
15
votes
0answers
378 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
...
14
votes
1answer
346 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 ...
14
votes
2answers
380 views
How can I speed up the classic GA for graph coloring?
I'm trying to compute the chromatic number of this graph (which is 28):
g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col";
My genetic ...
12
votes
3answers
489 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 ...
12
votes
4answers
1k 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 ...
10
votes
4answers
344 views
Finding Local Minima / Maxima in Noisy Data
I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
10
votes
2answers
350 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 ...
9
votes
3answers
234 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 ...
9
votes
2answers
395 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:
...
8
votes
1answer
500 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:
...
8
votes
1answer
905 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). ...
7
votes
4answers
194 views
NMinimize usage
I would like to minimize functions including the following.
NMinimize[{1 - (1 - 1/n)^x - x/n, n > x, x > 1}, {n, x}]
However Mathematica complains about ...
7
votes
1answer
141 views
Efficiently filling area with disks located at certain points
Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
7
votes
1answer
410 views
How to speed up Minimum Spanning Tree algorithm?
How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here.
The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
7
votes
3answers
201 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.
...
7
votes
1answer
341 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 ...
6
votes
2answers
562 views
Implementation of a new Game of Life Rule
I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action.
I would like to implement the ...
6
votes
2answers
161 views
Built-ins for discrete ArgMax or ArgMin?
Wondering whether there are discrete versions of ArgMax / ArgMin, that is, something that will find the part of an expression at ...
6
votes
1answer
215 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 ...
5
votes
3answers
371 views
Travelling salesman with start and end points for 30 points
I am doing a route optimisation for delivery vehicles and failing dismally. Please see problem statement below. My current solution uses FindShortestTour, but this does not have defined start and end ...
5
votes
2answers
257 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 $A[0]$.
...
5
votes
1answer
248 views
Defining a non-linear optimization-problem
Consider the following non-linear optimisation problem:
...
5
votes
2answers
153 views
5
votes
1answer
323 views
Multi-objective genetic algorithm in Mathematica?
Is there any implementation of a multi-objective genetic algorithm for Mathematica?
5
votes
1answer
122 views
FindMaxValue specifics
I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
5
votes
0answers
194 views
Mathematica vs Sigmaplot (Non LinearModelFit)
I asked a question in a previous post that was closed because "The title of the question is not correct and the issue here is too trivial to help anyone later".
NonLinearModelFit
It's possible ...
4
votes
1answer
153 views
Maximizing functions with Which statements
I'd like to be able to find the maximum value that my Capex function (see below) generates. This is a fairly simple function so I could just add it up but I have more complex functions of a similar ...
4
votes
1answer
302 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:
...
4
votes
1answer
171 views
Optimizing a rank 3 tensor
Assume we have the following elements
\begin{equation}
F_i{}^j \;and\; S_{ij}{}^k,
\end{equation}
which represent the components of tensorial objects of ranks 2 and 3 respectively, with Complex ...
4
votes
1answer
161 views
Why is this minimization with Boole functions failing?
I am running this command in Mathematica 8.0.4.0:
...
4
votes
1answer
225 views
4
votes
1answer
73 views
Minimize failing on a polynomial
Calling:
Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2,
0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}]
returns ...
4
votes
1answer
136 views
Assumptions seem not to be considered
In the following a,b is a probability distribution, i.e. a+b==1 with ...
4
votes
0answers
75 views
When using NMinimize[…,Method->“DifferentialEvolution”] is an “iteration” different than a “step”?
Hopefully this question has a simple answer. I have the following bit of code:
...
4
votes
0answers
97 views
Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events
The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
3
votes
3answers
221 views
How to find the minimum of this constrained expression?
Let $x$, $y$, $z$ be three nonegative real numbers and $x^2 + y^2 + z^2 = 5.$ Find the minimum of the expression
$$E=\dfrac{1}{2}x^2 y^2 + y^2 z^2 + z^2 x^2 + \dfrac{96}{x + y + z + 1}.$$
I tried
...
3
votes
2answers
457 views
optimization problem with NDSolve
I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct:
...
3
votes
1answer
286 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:
...
3
votes
2answers
182 views
Find all points that have the same minimum? [duplicate]
Possible Duplicate:
How to find all the local minima/maxima in a range
Sin[x] have two points ($3\pi/2,7\pi/2$) where the same minimum ($-1$) is achieved ...
3
votes
1answer
99 views
Distance between two functions satisfying a constraint
My problem is that I have two functions that are described as follows:
...
3
votes
1answer
214 views
wrong use of _?NumberQ?
I am having trouble with a numerical exercise. Here's a simplified version of my problem.
I define two functions to find the solution to two constrained maximization problems:
...
3
votes
2answers
90 views
Find condition under which variables fall away
I have a somewhat lengthy expression, looking like
expr = 1 + x + b + Pi + 2*a
Is there some way of generating a relationship between ...
3
votes
1answer
329 views
How to use mathematica to create school time-table?
I wonder if it is possible to use Mathematica for helping myself to create school timetable. I have a feeling that it requires quite simple optimization algorithm, but I have never been into ...
3
votes
1answer
223 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 ...
3
votes
0answers
177 views
What in practice is the difference between NMaximize[] and FindMaximum[]? [closed]
NMaximize[f,x] maximizes f numerically with respect to x.
...
3
votes
0answers
163 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?
