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

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240 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
134 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
248 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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1answer
285 views

Visualization of iteration procedure in NMinimize

I have this optimization code: ...
5
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1answer
152 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
5
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2answers
105 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
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2answers
152 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
216 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
307 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
99 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
93 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. ...
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0answers
129 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
141 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
616 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
283 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
532 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
161 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
258 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
825 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
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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1answer
197 views

Why is this minimization with Boole functions failing?

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

Finding minimal distance between two surfaces

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

Using compiled function inside NMinimize

Consider this code: ...
4
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1answer
319 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
163 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
214 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
2answers
94 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 ...
4
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1answer
60 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
124 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
260 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
511 views
4
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1answer
116 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
88 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 ...
4
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2answers
261 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
votes
1answer
115 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
votes
1answer
114 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
votes
3answers
262 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
235 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 ...
4
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1answer
183 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 ...
4
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1answer
392 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}} - ...
4
votes
1answer
247 views

Assumptions seem not to be considered

In the following a,b is a probability distribution, i.e. a+b==1 with ...
4
votes
1answer
303 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
4
votes
1answer
268 views

Ordinary differential equation invloving the function composition

I want to solve the following function: DSolve[(A1*Exp[B1*f[x]] + A2*Exp[B2*f[x]])*f'[x] == A1*Exp[B1*x] + A2*Exp[B2*x], f[x], x] And this is what I get as an ...
4
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1answer
183 views

Forcing optimal solution for FindShortestTour

I use FindShortestTour as explained here and it works nicely for a small number of cities. However when I try this with as little as 16 cities, the given tour isn't ...
4
votes
1answer
551 views

FindMinimum, NMinimize, etc. with external process

I was hoping to be able to use MMA's minimization power to work with an external process. I want to minimize the function 'TryThisNumber[x_]' which sends the value of x to something external and gets ...
4
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1answer
92 views

Why does EvaluationMonitor in FindMaximum only work for some regions?

This has come about after trying to understand what was going on with this question about FindMaximum and regions. My first thought in that scenario was to set-up ...
4
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1answer
120 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...
4
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1answer
68 views

`FindMinimum` with compiled function [duplicate]

I don't know how to fix this problem: ...
4
votes
1answer
102 views

Sparse Hessian for FindMinimum? Broken?

Is the sparse Hessian mechanism for FindMinimum[] (Method->"Newton") broken? Or am I simply not apprehending its proper setup? Here's what's happening. Below is for solving the example problem ...
4
votes
2answers
120 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.: ...