# Questions tagged [mathematical-optimization]

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

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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 ...
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 <...
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 ...
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 ...
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 ...
2k views

### How to work with ExperimentalNumericalFunction?

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 ...
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 ...
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 ...
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 ...
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 <...
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. ...
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] ...
357 views

### ExperimentalNumericalFunction in NMinimize solution

I try to make a number of optimizations using this code: ...
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 ...
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 ...
930 views

### Trouble with NMaximize

I am having trouble with maximizing a function I am interested in. Below is the code I am using. ...
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 ...
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 ...
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 ...
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 ...
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[][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution ...
128 views

### LinearProgramming behavior

Consider the following linear programming problem: ...
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 ...
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 ...
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: ...
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 ...
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 ...
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? ...
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). ...
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### 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, 1 + Pi/10]. The correct ...
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 ...
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 ...
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 ...
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: ...
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 ...
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} ...
854 views

### How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
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 ...
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 ...
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 ...
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. ...
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### 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: ...
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, ...
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 ...
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 ...
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_{...