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

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4answers
456 views

Minimal overlap area of circles

I have 20 points in the 2D plane with $(x_i,y_i)$ coordinates. I want to use Mathematica to optimally distribute 10 circles with equal radius of a given positive value $R$, i.e. to determine with the ...
5
votes
2answers
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
329 views

Finding minimum and maximum of implicit functions

The equations of the system are ...
5
votes
1answer
288 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
votes
2answers
374 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
votes
2answers
526 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
787 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
votes
3answers
282 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
votes
2answers
155 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
votes
1answer
251 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
votes
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
votes
1answer
304 views

Visualization of iteration procedure in NMinimize

I have this optimization code: ...
5
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2answers
103 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
votes
1answer
161 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
5
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2answers
154 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
votes
2answers
114 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
166 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
270 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
votes
1answer
314 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
5
votes
1answer
104 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
53 views

“PostProcess” and “Tolerance” in DifferentialEvolution? [closed]

What is "postprocess" option in DifferentialEvolution method (for instance when using ...
5
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0answers
209 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
160 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
votes
0answers
286 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
votes
0answers
165 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
843 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: ...
5
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0answers
669 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
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 ...
4
votes
3answers
571 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
votes
1answer
175 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
329 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
votes
1answer
363 views

$L_\infty$ norm minimization

I write supplemental explanation to render my aim of optimization. First Consider discrete time linear system below: \begin{equation} G(z)=\frac{1-e^{-0.3T}}{z^{100}(z-e^{-0.3T})} \end{equation} ...
4
votes
1answer
906 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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1answer
89 views

Writing a function that finds the difference between two maxima

Suppose i have two functions: $\qquad -2x^2 +5x+3$ and $\qquad -5x^2 +2x+3$ To solve the point where the functions are at maximum i use the command NMaximize ...
4
votes
3answers
319 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
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 ...
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
198 views

Why is this minimization with Boole functions failing?

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

Finding minimal distance between two surfaces

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

Using compiled function inside NMinimize

Consider this code: ...
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 ...
4
votes
1answer
171 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
votes
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
76 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
169 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
votes
1answer
274 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
votes
1answer
603 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
votes
2answers
278 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 ...