Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
1,355
questions
1
vote
1answer
132 views
Moving the start of a graph to the right, finding maxima in an oscillator
I have the following code written to simulate a driven damped oscillator
...
4
votes
3answers
776 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 <...
3
votes
1answer
623 views
Numerical Instability?
Current Status
Please skip ahead to Update 2: the key questions are now:
1/ Why does Mma generally fail to find the minimum for a well behaved function when the function does not have infinite ...
-1
votes
1answer
153 views
How to fit one parametric array to another numerical array?
I have two arrays of length n. One of them is obtained by experiment, so every element of
the array is a number. The other array is parametric, each element is a ...
1
vote
0answers
44 views
$H_{\infty}$ optimization of transfer function matrix [duplicate]
I have a two-dimensional $(2 \times 2)$ transfer function matrix like this:
$$G(s) = \begin{pmatrix}
\frac{1}{xs+1} & \frac{1}{s+0.5}\\
\frac{3}{s+3}& \frac{1}{ys+2}
\end{pmatrix} $$
The ...
39
votes
1answer
2k views
How to work with Experimental`NumericalFunction?
This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?"
Oleksandr R. correctly states in the comment:
A ...
1
vote
0answers
210 views
Increase optimization processing speed
As you know, sometimes numerically solving of optimization problems takes several minutes. For this reason 2 question came up to me:
1 - When one is abort the optimization procedure, how it is ...
8
votes
2answers
579 views
Numerical Optimization Methods
I am curious if any one has comments on "specific characteristics" of a problem that will deem it to be best solved by a specific optimization method such as ...
8
votes
1answer
648 views
NMinimize go out of bounds on some linear constraints
I'm trying to minimize a non-linear function of four variables with some linear constraints. NMinimize on Mathematica 8 seems to go out of bounds on some constraints giving complex values of the ...
3
votes
1answer
141 views
Bug with LinearProgramming on Integers?
With Mathematica 7:
LinearProgramming[{1, 1}, {{0, 0}, {1, 1}}, {1, 1}, Automatic, Integers]
gives wrong result {0,1}. But
<...
0
votes
1answer
1k views
NMinimize to optimize function Module
I am using Nminimize for simulation based optimization. I define the objective function (simulation with a variable "a") as a module to be used in the minimization. ...
1
vote
2answers
225 views
Minimizing the maximal residual in mathematica
With this:
d1 = 10; d2 = 4;
mat = RandomReal[{-1, 1}, {d1, d2}];
vec = RandomReal[{-1, 1}, d1];
LeastSquares[mat, vec] ...
11
votes
1answer
357 views
Experimental`NumericalFunction in NMinimize solution
I try to make a number of optimizations using this code:
...
6
votes
0answers
459 views
Simulated Annealing Parameters and Results [closed]
I am using SimulatedAnnealing method for a simulation based optimization problem and was wondering if someone can enlighten me on the following features:
Is there ...
10
votes
1answer
1k views
Simulated Annealing Convergence
I am using Simulated Annealing method for a simulation based optimization of a process that has 3 variables, using NMinimize.
I print the input/output during every ...
0
votes
1answer
930 views
Trouble with NMaximize
I am having trouble with maximizing a function I am interested in. Below is the code I am using.
...
4
votes
2answers
307 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
votes
2answers
1k views
How to find the maximum of this function on the positive real line?
I need to maximize this function on the positive real line:
$$
\frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x}
$$
the correct answer should be ...
11
votes
1answer
275 views
DifferentialEvolution scaling factor randomization
Using NMinimize for finding global minima, one can choose the DifferentialEvolution method. You can find a (not so) detailed ...
3
votes
2answers
2k views
Convert number to exponent form with highest power possible
As a school assignment we have to write a program which solves this issue. Since the program has to run efficient I am wondering what the best way is to approach this issue. Of course there you can ...
0
votes
0answers
318 views
Maximum of NDSolve output. Problem with interpolating function
I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables.
Now, I would like to get a distribution ...
0
votes
1answer
128 views
4
votes
3answers
441 views
Fastest way to check if an expression contains all symbols from a list
I need to execute this function thousands of times, and the faster, the better. I came up with two versions, but wanted to see if you can come up with an even faster way. Is there a better way?
I use ...
5
votes
0answers
281 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 ...
1
vote
1answer
491 views
Domain errors with Maximize/NMaximize
I am trying to maximize a (somewhat) complicated function over probability distribution $p$ and $q$. Here is my input:
...
0
votes
1answer
174 views
Maximization of a function within a unit square [closed]
I work in a unit square. I have some conditions under which areas within the unit square are defined. Say for simplicity that there are two conditions which define two areas. For example, if y > 1/2 ...
1
vote
1answer
789 views
Numerical saddle point problem of a function of many variables
I want to find the following saddle point of the function of 10 variables:
.
I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
1
vote
1answer
1k views
Symbolic Constrained Optimization
I have a question regarding evaluating constrained optimization problems in symbolic terms. I would like to perform How can I implement the method of Lagrange multipliers to find constrained extrema? ...
3
votes
1answer
903 views
Find Chebyshev center of a region by optimization
Let's consider a region like this:
The aim is to find the "Chebyshev center" of the region. By using the polygons, one can approximate the perimeter of region by an $n$-gon ($n$ is large enough). ...
1
vote
1answer
96 views
2
votes
1answer
1k views
Finding exact local extrema of simple functions
I want to exactly find all the local maxima of
f[x_] := x^4/4 - x^2/2
over the interval [-Sqrt[2], 1 + Pi/10].
The correct ...
2
votes
0answers
256 views
Combination of linear programming with bilevel optimization
I'm not a programmer really (interested in mathematics actually). Excuse me if I can not coding good. I'm also interested in implementation of mathematics results in programming language. That's my ...
2
votes
1answer
180 views
NMaximize and Accuracy
I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
3
votes
2answers
563 views
Is it possible to monitor the sum of squared errors in a NonlinearModelFit or FindFit procedure during the process?
Since fitting procedures using NonlinearModelFit (or FindFit) sometimes take very long, I would like to monitor the sum of ...
7
votes
1answer
318 views
Large scale linear programming (Data imported from .mat file)
I tried to run a large scale linear programming with mathematica.
I entered the code below:
...
3
votes
1answer
205 views
Mathematica Library
I created a Mathematica packagr and then I used the Needs function to add the library to my .nb file, but when use a function in my .nb file and the function is built in my library it comes up with ...
4
votes
1answer
492 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}
...
1
vote
1answer
854 views
How to perform a symbolic minimization?
Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ?
...
26
votes
2answers
2k views
Schedule programing problem with integer linear programming
I know how to model this question on paper, but I don't know how doing it in Mathematica.
Imagine , there is a university student who want to choose courses for this semester and he got the ...
0
votes
0answers
65 views
Compiling Visual Studio C++ to Run on Computers without Mathematica [duplicate]
I have written a console application on Visual Studio C++ as below
...
10
votes
3answers
1k views
How can I complete a correlation matrix with missing values?
I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
12
votes
1answer
1k views
Fitting Vogel's formula for phyllotaxis to the image of a flower
After having read this question I was inspired to investigate how we could take an image of a plant displaying phyllotaxis and fit Vogel's model of phyllotaxis to the image. The theory is very simple.
...
2
votes
1answer
167 views
Declaration of variables in large Linear Programming model with NMaximize
I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem:
$$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\
s.t\quad
\...
3
votes
1answer
201 views
Decomposing a diagonal positive real matrix
I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$:
$$E = \left(
\begin{array}{ccc}
0 & & & \\
& a & & \\
&...
6
votes
0answers
202 views
Issue with FindCurvePath
I have a problem with the function FindCurvePath. In some cases it crashes the Mathematica 9 Kernel. Here an example, where it crashes the kernel:
...
1
vote
1answer
282 views
NMinimize stops with no more memory?
I am using NMinimize function for simulation based optimization. So my objective function is a simulation that runs for every combination of variable values evaluated by NMinimize function. However, ...
4
votes
1answer
853 views
Arnold's problem #8
The famous Arnold's problems (see
http://www.math.upenn.edu/Arnold/Arnold-Trivium-1991.pdf ) are
aimed at the strong graduate and postgraduate students of the top universities.
I find it remarkable ...
27
votes
2answers
6k views
Optimization of a portfolio of stocks
I would like to use Mathematica to perform an optimization of a portfolio composed by 10 stocks. I did the first part to compute yields and expected yields, but I don't know how to finish the ...
4
votes
1answer
563 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 ...
1
vote
0answers
467 views
Minimizing a functional takes forever
I need help with minimizing a functional in Mathematica.
I have a function $V(\xi)=\sum_{i=1}^\infty C_{3_i}J_0(\xi/C_i)+C_{4_i}Y_0(\xi/C_i),~~~\Sigma\leq\xi\leq\xi_1$, and want to find such $\{C_{...
