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

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2
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1answer
3k views

Using NonlinearModelFit to fit data with errors

Assume we have some data of measurements SeedRandom[9]; data = Table[{i,2*(1 + 5*RandomReal[])*Exp[-0.01*(1 + RandomReal[])*i]}, {i, {0, 100, 200, 400, 700}}]; ...
3
votes
2answers
512 views

Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
2
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0answers
317 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
2
votes
0answers
329 views

Why my Mathematica 9.0.1 wont work with some samples of Mathematica in Graph Theory?

Bug introduced in 9.0 and fixed in 10.0 FindMinimumCostFlow is introduced in 9.0. I updated my Mathematica recently to 9.0.1 cause the previous version was ...
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0answers
46 views
5
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0answers
842 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: ...
2
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1answer
525 views
2
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1answer
260 views

How can I change the MPS format in Linear Programming samples of Mathematica?

I am trying to play with some linear programming examples of Mathematica as ExampleData[{"LinearProgramming", "blend"}, "Equations"]. It gives me the MPS format of ...
4
votes
1answer
190 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 ...
2
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1answer
270 views

List comparison in constraints for Minimize

I am trying to solve an optimization problem, a simplified version of which is as follows: ...
4
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3answers
570 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
1answer
218 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
4
votes
1answer
408 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - ...
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 ...
2
votes
1answer
460 views

How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? ...
1
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1answer
2k views

How to find the global maximum of a function? [closed]

I tried the following but plotting the function clearly reveals that there is a global maximum around $r = 7$ (here $a = 0.53$) ...
4
votes
1answer
1k views

Inequalities with assumptions and constraints

I'm using Mathematica 8 I've been searching the net without luck for this specific solutions: Suppose I have an inequality f(x;M,m)>0 where I KNOW that M>4m and m>0. How can I let Mathematica know ...
1
vote
2answers
764 views

Area of the largest rectangle bounded by $y=x^2$ and the x-axis within the unit interval

I am trying to find the area of the largest rectangle (whose sides are parallel to the coordinate axes) contained in the region bounded by the graphs of $y = 0, y = x^2,$ and $x = 1$ using ...
6
votes
1answer
369 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
10
votes
1answer
355 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 ...
2
votes
1answer
122 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
2
votes
2answers
318 views

NMinimize problem again

Following up my previous question which got great replies, I am now trying to do ...
9
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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 ...
0
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1answer
489 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
4
votes
4answers
287 views

How can I name “a[[i]]” the parts of Table “a”? Or how to make Table “a” grow inside FindMinimum?

Let's say I want to minimize a function that uses a Table named a with the Conjugate Gradient Method of ...
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
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1answer
2k views

Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
0
votes
1answer
227 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
0
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1answer
100 views

Error with minimization of NProbability

I'm trying to solve the following problem: ...
2
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1answer
741 views

Problem using the DifferentialEvolution method of NMinimize [closed]

I have a function of 20 parameters, which 3 of the parameters are my physical parameters, and the others are pull terms to fix the errors. The goal is finding the global minimum of this function, to ...
0
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0answers
748 views

Mathematica, nested optmization [duplicate]

I want to use the solution of Maximize, defined as a function, in another function. Here's an example: ...
6
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1answer
482 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
2answers
162 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 ...
8
votes
3answers
912 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 ...
1
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0answers
135 views

How to express this output in the form $X=A.x$?

This problem arose in my stereo vision project. I have two matrices: $$ A = \left( \begin{array}{ccc} \text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & ...
1
vote
1answer
167 views

Seemingly simple optimization problem is slow

I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so: ...
1
vote
1answer
416 views
0
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1answer
391 views

Finding resolution of an optical system using Rayleigh criterion

I want to use the Rayleigh criterion to find the resolution of an optical system. I have two functions f1 = Sinc[x]^2 and ...
1
vote
1answer
681 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
1
vote
0answers
66 views

Using lists as optimization parameters [duplicate]

Possible Duplicate: Minimizing a function of many coordinates Suppose that the function $F[\vec{x}]$ computes a certain polynomial of the elements of the list $\vec{x}$. How can I use ...
5
votes
1answer
314 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
2
votes
0answers
516 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
16
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2answers
556 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, ...
2
votes
1answer
762 views

Restrictions problem

I tried to program a simple linear optimization model and don't know where my mistake lies. The function should be a sum over "t" and "z" from the product of two constants ("e" and "H") and the ...
4
votes
3answers
2k views

Determining the local extrema of discrete data [duplicate]

Possible Duplicate: Local max/min of Mathematica data sets If I have a continuous function f (for example ...
4
votes
1answer
334 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 ...
1
vote
1answer
1k views

How to find local minima of a multivariate function with singularity?

I am working on a logistic regression problem which requires minimizing a cost function J[{theta0, theta1, theta2}, X, y] to find the optimal value for fitting ...
2
votes
1answer
409 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
17
votes
2answers
856 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 ...
2
votes
1answer
1k views

FindMaxValue and FindMaximum - how to find GLOBAL maximum and not just LOCAL maximum

I will not be able to provide a simple minimum working example here as this seems to be very specific. I have an interpolating function which I substituted into a PDE and then plot said PDE at a ...