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

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185 views

Finding the maximal `t` at which `u[x,t] == 1`?

Given the smooth function u[x,t] on a domain, how do I find the maximal t at which ...
5
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2answers
315 views

Finding minimum and maximum of implicit functions

The equations of the system are ...
5
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1answer
283 views

Is there any strategy to have a compiled version of FindFit or NonlinearModelFit?

Disclaimer: This is not a precise question with a definite answer. I know that neither FindFit nor NonlinearModelFit is in the ...
5
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2answers
371 views

Optimum number of cog teeth for two step helical gearbox

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I. I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
5
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2answers
525 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
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1answer
777 views

Packing squares into a circle

I am currently trying to solve and understand a problem about packing the maximum of squares into a circle. What I am trying to do, is to calculate the maximum number of variable sized squares (with ...
5
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3answers
273 views

Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...
5
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3answers
273 views

Indicate minimal path sum

Described on the page: http://www.mathblog.dk/project-euler-81-find-the-minimal-path-sum-from-the-top-left-to-the-bottom-right-by-moving-right-and-down/ It is an example of the solution indicated in ...
5
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2answers
153 views

Techniques to find all local minima of black box function with n continuous derivatives?

I have a blackbox function f on [a,b] that is known to be continuous, and has n continuous derivatives. The function uses polynomial interpolations (but isn't a polynomial interpolation itself), so no ...
5
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1answer
250 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 ...
5
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2answers
99 views

How to find alignments of interlocking shapes?

I'm searching for the ways to align interlocking shapes, that is, finding the locations and rotations that maximize the arc length at which they touch. For simplicity, I'm assuming 'shapes' are one ...
5
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1answer
298 views

Visualization of iteration procedure in NMinimize

I have this optimization code: ...
5
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2answers
100 views

Parallel function evaluation for minimal value

I am asking myself, if the evaluation of a function f looking for a minimal value over a discrete set of values can be parallelize (brute scan for a potential ...
5
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1answer
159 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
5
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2answers
147 views

NMinimize in one-dimensional Interval

An Interval should be a one-dimensional region, so a region. I tried to minimize a function over an interval, e.g.: ...
5
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2answers
113 views

Optimization problems over the Integers

Should be an easy question. How can I define a function which gets only integers in a form that I can use to find max and min for instance? Example: Find the Max of the expression ...
5
votes
2answers
163 views

Optimizing code containing an infinite sum

I have the following expression. It's based on the negative-log-likelihood of a Poisson-Gaussian noise model, i.e. a convolution of a Poisson & Normal distribution. The value $x_{i}$ is the ...
5
votes
1answer
263 views

Slow-down encountered when using NMinimize with a compiled function

I'm minimizing a large function. Evaluating the function is very slow symbolically but using Compile I can get ~100x speed-up on this step. However, despite this, the NMinimize process is only ...
5
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1answer
313 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
5
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1answer
101 views

Simple minimization not evaluating

I tried to solve a rather simple optimization problem, which Mathematica apparently cannot handle. A minimal example is the following: ...
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0answers
204 views

Visualizing the Lagrange Multiplier Solution

This question is based on work in Susan Colley's Vector Calculus, 4th ed. The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint ...
5
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0answers
94 views

How to perform Bayesian optimization with Mathematica? [duplicate]

Does Mathematica have any Bayesian optimization methods for learning hyper-parameters? Practical Bayesian Optimization of Machine Learning Algorithms Jasper Snoek, Hugo Larochelle and Ryan P. ...
5
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0answers
149 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
5
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0answers
270 views

Packages for Semidefinite programming

This question has already been asked here. I am not sure, whether I should have asked this question as a comment of an old question or in the general programming forum of stackexchange. Moderators ...
5
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0answers
152 views

NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
5
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0answers
660 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?
4
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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 ...
4
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3answers
562 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 ...
4
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1answer
173 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
4
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2answers
317 views

Maximization in Mathematica using matrix and vector notation

I am trying to solve a simple maximization problem in Mathematica, using matrix and vector notation. ...
4
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1answer
890 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
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3answers
315 views

FindRoot constrained to maximum

I am using FindRoot to find the local maximum op some function, by examining where its derivative is zero. However, keeping the starting value the same, sometimes ...
4
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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 ...
4
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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
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1answer
198 views

Why is this minimization with Boole functions failing?

I am running this command in Mathematica 8.0.4.0: ...
4
votes
2answers
610 views

Finding minimal distance between two surfaces

This code will display two parametric surfaces: ...
4
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2answers
500 views

Using compiled function inside NMinimize

Consider this code: ...
4
votes
1answer
333 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
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1answer
170 views

Goal optimization: finding the best combination of capacitors and resistors resulting in given properties

I want to edit @MarcoB answers (because the code he gave doesn't answer the question appropriately)->(the function that need to be optimised is not implemented as asked) But it seems like I am having ...
4
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1answer
218 views

How to solve this simple equation?

I want to minimize a quadratic equation, but Mathematica does not solve it and only rewrites the solution. I wonder if there exist any way I can skip the computation by hand (I can solve it using ...
4
votes
1answer
75 views

How to get function output with Manipulate

I have a program, which makes Gauss-Jordan transformations (not too pretty, I suppose). I want to get output with Manipulator like that: Two-Phase Simplex Method with only "step number" slider. One ...
4
votes
2answers
160 views

FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)

I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize. In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
4
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1answer
271 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=\max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions ...
4
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1answer
579 views
4
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1answer
118 views

Exiting FindMinimum when a condition is met

I want to determine if a function f[x] can take negative values. f is expensive to compute and ...
4
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2answers
276 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
4
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1answer
117 views

Question about FindMaximum

I must advise you that I am an almost total novice in mathematica.. However here is my very simple question.. I know the command FindMaximum[{f},{x}] to find the maximum point and maximum value of a ...
4
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1answer
127 views

What is the status of the FindMinimum method “QuadraticProgramming”?

As a method option to FindMinimum "QuadraticProgramming" is still a valid option. It has the advantage of being significantly ...
4
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3answers
295 views

How to fit parameters in a system of coupled differential equations

Problem description: I'm studying a chemical reaction that can be modeled by a system of coupled differential equations, and I want to use measured data to determine the parameters that appear in the ...
4
votes
2answers
244 views

How to set up and minimize a large system of equations to resolve the individual components

I am trying to set up a system of 400*N equations to deconvolute spectral data for four different compounds. I monitored 400 different wavelengths in N solvents (3 solvents in this case). In order ...