Questions tagged [mathematical-optimization]

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

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168 views

Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
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0answers
324 views

NMinimize: Problem with constraints + Simultaneous minimization possible?

Introduction Dear all, I am fairly new to Mathematica. Recently I am trying to do the following: I have a function $$\textrm{hann}[t,t_g,n_m]=\sum\limits_{n=1}^{n_m}a_n\left[1-\cos\left(\frac{2\pi ...
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3answers
770 views

Not able to get a solution to a Lagrange Multiplier Equation

I assigned several constrained optimization problems to my calc IV students to solve with Mathematica, but this one is being stubborn. The function to optimize is: f(x,y,z) = y Exp[x-z] with the ...
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2answers
731 views

Maximizing a trigonometric function

This is probably a naive question, but here it goes: I know that $$r\cos a+s\cos b+t\cos c \leq \frac{rs}{2t}+\frac{rt}{2s}+\frac{ts}{2r},$$ subject to the conditions $a+b+c=\pi$ and $r,s,t$ are ...
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1answer
2k views

Working precision and pure functions in FindMinimum

I have this function: fun = (# - 5.0)^2.0 & Then, I want to find the minimum: ...
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1answer
142 views

How can I find the greatest of this expression?

I want to find the greatest of the expression $$P=a \sqrt{12-b}+\sqrt{b\left(12+a^2\right)}+66\sqrt{a^2+b+3}-\left(a^2+b\right)^2$$ with $a >0$, $0<b\leq 12$. I tried ...
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0answers
86 views

NMaximize : constraint violation [duplicate]

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3answers
940 views

How to use a compiled function in numerical optimization

I'm trying to wrap my head around function Compile. So, this is a spin-off question from: a previous question on using compile[] correctly. I have a function that ...
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1answer
353 views

How to get NMinimize to work

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1answer
229 views

Getting standard errors (Hessian matrix) from optimization with constraints

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1answer
632 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
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4answers
1k 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 ...
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1answer
174 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 ...
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0answers
78 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
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2answers
319 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 ...
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1answer
89 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. ...
5
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1answer
171 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 ...
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3answers
618 views

Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
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0answers
165 views

NMaximize stops evaluating my function when run in parallel [closed]

I am trying to maximize the results of a Monte Carlo simulation with respect to some input variables. ...
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0answers
991 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 $k$ ...
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124 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 ...
19
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2answers
7k 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
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0answers
90 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: ...
2
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1answer
666 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. ...
7
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2answers
1k views

Using compiled function inside NMinimize

Consider this code: ...
2
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1answer
503 views

How to minimize a list of data points?

I have a list called diff1: ...
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1answer
540 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, ...
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0answers
616 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 ...
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1answer
232 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, here'...
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1answer
220 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. ...
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1answer
153 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 ...
33
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1answer
2k 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 ...
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0answers
36 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 ...
2
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2answers
487 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 ...
2
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1answer
140 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 ...
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0answers
901 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, ...
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1answer
261 views

Simulated Annealing for NMinimize[] always returning the same solution

I have a function defined as follows: ...
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1answer
95 views

Cannot save array to CSV file from EvaluationMonitor[]

Here is my Mathematica function. ...
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3answers
1k views

How to find local minima of data using PeakDetect

One of the great new function in v10 is PeakDetect. It can detect peaks (local maxima) according to desired sharpness as shown in this example: ...
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3answers
225 views

Optimization Algorithm: ideas wanted

EDIT: Lets assume a random matrix: ...
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0answers
384 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 ...
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1answer
559 views

Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
6
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2answers
292 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 $1,2,3,4,5,\ldots$...
13
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9answers
5k 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
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1answer
100 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 ...
2
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0answers
590 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
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1answer
343 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 ...
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0answers
504 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
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1answer
339 views

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

Why is the Out[74] not {1 - a, {x -> -1}}? ...
2
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2answers
1k views

Find the values of 3 variables that best fit 6 equations [duplicate]

I have 6 equations ...

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