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

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71
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 ...
57
votes
5answers
14k 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 ...
43
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
38
votes
3answers
3k 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 ...
33
votes
5answers
8k 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 ...
24
votes
3answers
828 views

Exponential fitting - isn't actually a BUG there?

There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds ...
24
votes
1answer
671 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 ...
23
votes
1answer
830 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 ...
20
votes
2answers
777 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 ...
20
votes
2answers
423 views

Maximize[Cos[x - 1], x] is not evaluated

No explanation needed: Maximize[Cos[x + 1], x] Maximize[Cos[x - 1], x] producing ...
20
votes
2answers
363 views

Numerical optimal control

I was hoping to tackle optimal control using Mathematica in order to learn how I can use Mathematica's built in numerical integration and optimization functions together in order to solve an optimal ...
19
votes
2answers
979 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
1k 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
3answers
4k 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 ...
17
votes
2answers
839 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 ...
16
votes
2answers
541 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, ...
15
votes
2answers
2k 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 ...
15
votes
1answer
321 views

Bug in plotting function using FindMinimum?

Bug introduced in 10.0 and persisting through 10.3 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of ...
14
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 ...
13
votes
9answers
2k 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 ...
13
votes
2answers
1k 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 ...
12
votes
4answers
5k 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
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 ...
12
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: ...
12
votes
1answer
1k 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 ...
12
votes
1answer
1k views

Multi-objective genetic algorithm in Mathematica?

Is there any implementation of a multi-objective genetic algorithm for Mathematica?
11
votes
4answers
204 views

Constraint syntax compaction

Is there a more compact way to represent these constraints: NMaximize[{a+b+c,...
11
votes
2answers
480 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
2answers
2k 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: ...
11
votes
1answer
174 views

Constrained optimization with three variables

A standard optimization problem in economics is choosing a consumption bundle subject to prices and a budget constraint: $$\max_{x,y} \sqrt{x} + \sqrt{y} \hspace{1cm} \text{s.t. } p_x \cdot x + p_y ...
10
votes
3answers
461 views

Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
10
votes
1answer
562 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. ...
10
votes
3answers
198 views

How to describe the convex hull of a set of points as an implicit region for optimization?

Last edit: 2016-05-03 A.G.'s answer was the one helped me the most, see explanation at the end of this question. Original question In Mathematica you can create out of a set of points in 2D and 3D ...
10
votes
1answer
186 views

DifferentialEvolution scaling factor randomization

Using NMinimize for finding global minima, one can choose the DifferentialEvolution method. You can find a (not so) detailed ...
10
votes
1answer
706 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 ...
10
votes
3answers
666 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 ...
10
votes
4answers
326 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. ...
10
votes
1answer
398 views

Shortest tour with vertex priority

I changed the title of my question and tried to simplify formulation of the problem. I solve a very big vehicle routing problem. I divided this one big problem on many small sub-problems. Each small ...
10
votes
2answers
2k 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. ...
10
votes
0answers
274 views

PenaltyFunction Option in NMinimize

I am curious if anybody has some experience in using the built-in Option "PenaltyFunction" in any of the numerical optimization functions like NMinimize. According to the documentation the user ...
9
votes
2answers
3k views

Optimization of a portfolio of stocks

I would like to use Mathematica to perform an optimization of a portfolio composed by 10 stocks. I did the first part to compute yields and expected yields, but I don't know how to finish the ...
9
votes
3answers
477 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
1answer
749 views

Max & min distance between two moving points

I am trying to find the minimal and maximum distance between two moving points with Mathematica in an interval. For example, ...
9
votes
4answers
3k 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
492 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
341 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
2answers
1k views
9
votes
2answers
290 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
849 views

Simulated Annealing Convergence

I am using Simulated Annealing method for a simulation based optimization of a process that has 3 variables, using NMinimize. I print the input/output during every ...
9
votes
0answers
95 views

LinearProgramming returns an invalid null solution that apparently doesn't satisfy constraints without any warning

Bug introduced in 10.3.1 or earlier and persisting through 10.4.1 While searching to answer the question Solving the magic backyard puzzle with MMA at some time I composed a set of arguments ...