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

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7
votes
4answers
495 views

Finding the point of minimum distance between two parametric functions

I have two functions re and rm, for which I computed the minimum distance between them. Now I would like to add a point at the ...
3
votes
1answer
138 views

Calculate the relationship between the duration of two oscillating functions

I am trying to quantitatively determine the relationship between the length of two oscillating functions. Meaning, what is the duration of the green spike in relation to the blue square? Does anyone ...
1
vote
0answers
67 views

Optimizing evaluation of expressions dependent on four variables and containing double summation

I would like to optimize my code which I use to evaluate expressions containing double summation. These expressions are dependent on 3 space variables ($r$, $\theta$, $\phi$) and time $t$ and consist ...
5
votes
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 ...
1
vote
1answer
61 views

NMaximize not substutiting parameters of objective function [duplicate]

NMaximize is not substituting parameters of its objective function. Is there a way to fix that? I have a three line program that exhibits the problem. ...
4
votes
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 ...
1
vote
0answers
91 views

NMaximize stops evaluating my function when run in parallel

I am trying to maximize the results of a Monte Carlo simulation with respect to some input variables. ...
1
vote
0answers
377 views

Solving mixed integer programming using Mathematica

Let $x_{ij}$ be an $n\times k$ matrix defined as follows: $ x_{ij}=\begin{cases} 1, & \text{if }s_i\text{ is assigned to }S_j \\ 0, & \text{otherwise } \end{cases} $ and $S$ is a set of $k$ ...
3
votes
0answers
91 views

Efficient processing of Special Ordered Sets with LinearProgramming

I'm playing with integer linear programming, especially problems involving lots of constraints which would appear to be special ordered sets. Below is a toy example, three last rows of the matrix ...
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 ...
6
votes
0answers
80 views

Listable compiled functions used in NMinimize [duplicate]

This is an example from MMA: cListable = Compile[{x}, (x-1)^2, RuntimeAttributes -> {Listable}] In case of single entry: ...
17
votes
0answers
287 views

Can code optimize code?

Are there functions, programs or packages that deal with optimizing mathematica code i.e. re-writing ineffecive or convoluted code. -This question has haunted me since I joined SE. The background for ...
2
votes
1answer
254 views

How to build a list of constraints for NMinimize

Let's say I have aset = {-1, 0, 2}. I would like to create a variable Var that takes values from that set, i.e. ...
4
votes
2answers
460 views

Using compiled function inside NMinimize

Consider this code: ...
2
votes
1answer
108 views

How to minimize a list of data points?

I have a list called diff1: ...
2
votes
1answer
201 views

Finding the minimum of a function

I asked this question Mark Minimum Value in DensityPlot. Another question has come up, or better said, a task: Find the minimum of a function. I haven't been able to write the needed code for that, ...
2
votes
0answers
233 views

Maximizing Large Multivariable Function over Region with Parameter Constraints

Brand new Mathematica user here. I have a complicated function to maximize, and thought I would try software like Mathematica instead of taking derivatives by hand. I found some Mathematica ...
2
votes
1answer
130 views

Minimizing a function with some restrictions

I need help in finding a way to minimize a function with some complex constraints. I'm not an expert in this field, but I'm still trying to understand if I can do something with my problem. So, ...
1
vote
1answer
119 views

Manual maximum likelihood estimation of a mixture with no closed form

Let $X$ be a random variable that is from a mixture of two Lognormals (Lognormals(mu1,sigma) and Lognormals(mu2,sigma)) and set $Y=X_1+X_2+...+X_{10}$ a sum of 10 random variables from this mixture. ...
0
votes
1answer
91 views

Solving minimum length confidence interval problem

I'm trying to find the minimum length of a confidence interval for the variance from a sample iid with normal distribution. I tried ...
23
votes
1answer
752 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 ...
0
votes
0answers
34 views

What is that Root[…] inside the answer represent? [duplicate]

So I am encountering this situation, in which mathematica doesn't give me the answer, but in a form of "Root". How do I interpret this ? what is the number after the "&" represent? How should I ...
0
votes
0answers
108 views

Problems with NMinimize

I have written some functions that take a matrix and find its minimum inner product with a specific set of vectors ...
1
vote
2answers
206 views

Minimize loop optimization

I'm new in Mathematica 10. So far, I have a two variable-function and I've use Minimize to find the optimal solution. Nevertheless, I'd like to make a sensibility analysis and study how this optimal ...
1
vote
1answer
84 views

2D Arrangment/Optimization Problem

Okay, I have a list of angles, call it A. How would I arrange them in a 2D m-by-n grid G such that the distances between each adjacent angle-element (row- and column-wise) is minimized? G has as ...
1
vote
0answers
334 views

Speeding up NDSolve for system of differential equations

I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ...
0
votes
1answer
135 views

Simulated Annealing for NMinimize[] always returning the same solution

I have a function defined as follows: ...
0
votes
1answer
63 views
6
votes
2answers
385 views

How to find valleys of data using new function in V10 PeakDetect

One of the great new function in V10 is PeakDetect. It can detect peaks according to desired sharpness as shown in this example: ...
-1
votes
3answers
205 views

Optimization Algorithm: ideas wanted

EDIT: Lets assume a random matrix: ...
6
votes
0answers
284 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
7
votes
2answers
249 views

Using least independent rectangle area to separate every point

Description I want to add vertical line and horizonal lines between data to make every point have an independent rectangle area. In addtion, every independent rectangle has a number ...
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 ...
0
votes
1answer
77 views

Finding the right DeleteCases pattern for <<199>>

I have a list in Mathematica with several items like <<199>> and <<104>>, I would like to get rid of them using DeleteCases, but none of the patterns I ...
0
votes
0answers
160 views

How do I estimate the Pareto front in my multiobjective optimization problem?

I need to minimize a function of two parameters that gives two "stress" outputs {A,B} = f[tau,mu]. How do I estimate (even roughly), the Pareto front for this ...
0
votes
1answer
177 views

How to include constraints in `NMaximize`

I am trying to find maximum likelihood estimates of parameters for a fairly complicated multivariate distribution. The support of the distribution depends on its parameters so I need to include some ...
1
vote
0answers
235 views

Solve set of non-linear equations with least-squares-fitting - constrain results?

I'm trying to solve a set of functions to determine the material properties from a set of measurement values. (To set up this method I just want to fit my model with some already calculated data). My ...
6
votes
1answer
307 views

What is wrong about Abs[x]-a? Is it a bug?

Why is the Out[74] not {1 - a, {x -> -1}}? ...
2
votes
2answers
456 views
-7
votes
1answer
137 views

Mathemathica: How to plot diagram? [duplicate]

i want to plot a diagram by this command using mathemathica. but it plotted as a beeline while it must be have a bit aberration.what is my fault in plotting? i want to display my diagram such as ...
0
votes
0answers
76 views

NMinimize not starting [duplicate]

I am new to Mathematica so I might be asking a trivial question, although I wasn't able to resolve it for several days. I am trying to optimize a 7x7 matrix with 12 variables with a certain evaluation ...
2
votes
2answers
730 views

Maximum of Minimum of a two variable function

I have F[x, y] := (y/2)(2 Cos[2x] + 2 Cos[x] + 1)/5 + ((1 - y)/2)(2 Cos[x] + 1)/3. I am looking for the maximum of the minimum of ...
5
votes
3answers
922 views

Finding all maxima and minima of a function

To find all (global and local) extrema of a function in $\mathbb R^3$, I have written the following. Example function: ...
1
vote
1answer
63 views

What domain does Resolve assume by default?

Consider the statement: $\forall x\left(x<7\Rightarrow \exists a\exists b\exists c(a^2+b^2+c^2=x)\right)$ This is true provided the universe of discourse is $\mathbb{N}$ Now I use ...
0
votes
3answers
235 views

Why does Maximize return a wrong answer?

I want to find the maximum of the following function, but get a wrong result. What am I doing wrong? ...
1
vote
0answers
77 views

How to find a scaling parameter in matrix inversion process by MMA?

I simply would like to find the inverse of a given matrix $A$ by the iterative method $X_{k+1}=X_k(2I-AX_k)$ using $X_0=\frac{1}{\sigma_{max}^2}A^*$. An example is as follows ...
1
vote
0answers
59 views

A more efficient way of fitting a non-linear model that returns an entire list?

I have a function that takes two parameters, del and nu, and returns a list npoints long ...
1
vote
1answer
253 views

How to minimize the sum of squares of deviations from the mean?

I am trying to minimize the sum of squares of a deviation from the mean applying the following: Minimize[Sum[(Subscript[x, i] - μ)^2, {i, 0, n}], x] It returns ...
0
votes
0answers
68 views

Interpreting a certain result of Minimize

I am given a certain function $f(k_1)$ that I would like to minimize. Asking Mathematica to do it (and supplying the given bounds of other parameters in the expression) I get the following result: ...
1
vote
2answers
2k views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...