Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.

learn more… | top users | synonyms (4)

61
votes
2answers
5k 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 ...
50
votes
4answers
11k 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 ...
40
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
34
votes
3answers
2k 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 ...
24
votes
4answers
5k 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 ...
22
votes
1answer
483 views

How to work with Experimental`NumericalFunction?

This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?" Oleksandr R. correctly states in the comment: A ...
20
votes
1answer
564 views

Convex optimization

I am playing with some Compressed Sensing (think single pixel camera) applications and would like to have a Mathematica equivalent of a Matlab package call Convex Optimization (CVX). Specifically, I ...
19
votes
2answers
737 views

Schedule programing problem with integer linear programming

I know how to model this question on paper, but I don't know how doing it in Mathematica. Imagine , there is a university student who want to choose courses for this semester and he got the ...
19
votes
2answers
878 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 ...
18
votes
2answers
719 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 ...
17
votes
0answers
226 views

Can code optimize code?

Are there functions, programs or packages that deal with optimizing mathematica code i.e. re-writing ineffecive or convoluted code. -This question has haunted me since I joined SE. The background for ...
16
votes
2answers
718 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 ...
14
votes
3answers
2k views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
14
votes
2answers
443 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
13
votes
2answers
1k views

Find maximum value of interpolation function - obviously wrong result

Minimizing and maximizing interpolation function has already been asked and answered, see here for example. Yet, I observe a strange behaviour. Well, I can understand that the wrong guess of ...
13
votes
3answers
1k 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
4k 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 ...
12
votes
2answers
738 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 ...
11
votes
4answers
200 views

Constraint syntax compaction

Is there a more compact way to represent these constraints: NMaximize[{a+b+c,...
11
votes
2answers
320 views

Rotational Averaging of Image Periodograms (FFTS)

I'm writing a code to do rotational averages of image FFT's. I have a working version but it is pretty slow. Wondering if anyone has any thoughts on a way to do this more efficiently. Data looks ...
11
votes
1answer
2k 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: ...
11
votes
2answers
1k 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: ...
10
votes
8answers
1k views

Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
10
votes
3answers
328 views

Collatz optimization

I'm VERY new to Mathematica programming (and by new I mean two days), and was solving Project Euler question 12, which states: Which starting number, under one million, produces the longest ...
10
votes
2answers
407 views

What is the difference between FindFit and NonlinearModelFit

I cannot get the difference between these two fitting functions in Mathematica. I even read in MMA that the result of these two are the same.
10
votes
1answer
962 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 ...
10
votes
0answers
182 views

Bug in plotting function using FindMinimum?

Bug introduced in 10.0.1 (or 10.0.0) and persisting through 10.1 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of ...
9
votes
3answers
444 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
4answers
2k 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 ...
9
votes
3answers
436 views

FindShortestTour for charity (or: How can I optimize meal delivery with FindShortestTour?)

I've been wondering about this for a while - but never got around to asking - until I saw faleichik's incredible answer to Mathematica Minecraft. I did some work at a not-for-profit a little while ...
9
votes
1answer
2k views

Minimization by Nelder-Mead

Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...
9
votes
1answer
408 views

Fitting Vogel's formula for phyllotaxis to the image of a flower

After having read this question I was inspired to investigate how we could take an image of a plant displaying phyllotaxis and fit Vogel's model of phyllotaxis to the image. The theory is very simple. ...
9
votes
1answer
294 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 ...
9
votes
1answer
481 views

ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
9
votes
2answers
219 views

Relaxation of Mass-Spring System with Pinned Masses

Problem Assume that four masses are connected to each other by springs while two of them are pinned down at their initial positions. Find the position of masses when system is at its minimum ...
9
votes
1answer
1k views

Multi-objective genetic algorithm in Mathematica?

Is there any implementation of a multi-objective genetic algorithm for Mathematica?
9
votes
4answers
293 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
2answers
979 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 ...
8
votes
2answers
540 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
8
votes
3answers
497 views

How can I complete a correlation matrix with missing values?

I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
8
votes
2answers
957 views
8
votes
1answer
160 views

Experimental`NumericalFunction in NMinimize solution

I try to make a number of optimizations using this code: ...
8
votes
1answer
2k 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). ...
8
votes
2answers
1k views

Linear programming with many variables and parameters

I am trying to reconstruct the answer that is given in this report. (page 153 in Appendix B; Section B.2.1). They are given variables, parameters, constraints, and the objective function to minimize. ...
7
votes
3answers
2k 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 ...
7
votes
4answers
384 views

Finding the point of minimum distance between two parametric functions

I have two functions re and rm, for which I computed the minimum distance between them. Now I would like to add a point at the ...
7
votes
2answers
162 views

How to Maximize[Log[n]^(1/Log[n]), n]

I am new to Mathematica and am trying to work out how to use Maximize. Maximize[Log[n]^(1/Log[n]),n] Should give a solution at $e^e$. However in Mathematica you ...
7
votes
3answers
690 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 ...
7
votes
3answers
628 views

Cannot find the maximum value of a function

Consider the following function: $a Sin(x)+b Cos(x)$ I tried to obtain the maximum value of this function using MaxValue[]: ...
7
votes
1answer
117 views

Finding the least positive integer satisfying a quantified statement

I'm studying the convergence of the sequence of functions $f_n:[0,1]\subset\mathbb{R}\to\mathbb{R}$ defined by $$f_n(x)=n^2x(1-x^2)^n$$ for $n\in\mathbb{N}$. These functions converge pointwise to the ...