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

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LinearProgramming and Maximize giving different results [closed]

I'trying to do an embarrassingly simple linear programming problem, and being a total Mathematica and maths analphabet I'm stuck. The problem is to optimize (maximize) the function $1.2x+y$, with ...
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22 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 ...
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1answer
222 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. ...
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0answers
78 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 ...
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2answers
82 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] ...
2
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1answer
100 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 ...
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2answers
176 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 ...
4
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2answers
180 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 ...
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1answer
83 views

Trouble with NMaximize

I am having trouble with maximizing a function I am interested in. Below is the code I am using. ...
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0answers
78 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
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2answers
219 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 ...
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0answers
38 views

Faster evaluation of an expression for brute force optimization [duplicate]

I'm trying to bruteforce an optimization problem and I want to generate roughly a million function evaluations. I was wondering what would be the best for me to do in terms of having the expressions ...
3
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3answers
212 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 ...
4
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0answers
93 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 ...
0
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1answer
141 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: ...
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1answer
139 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? ...
0
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1answer
104 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
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1answer
135 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 ...
3
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1answer
280 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). ...
0
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1answer
137 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, ...
1
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1answer
158 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 ...
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0answers
150 views

CUDA 5.5 and Mathematica 9 code problem

In Mathematica 9, I entered the following sample code, but it returns an error. I can not figure what is not right. Any help? ...
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0answers
92 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 ...
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2answers
127 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 squared errors during the process ...
2
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1answer
243 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} ...
3
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1answer
139 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 ...
2
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1answer
108 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 ...
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2answers
448 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 ...
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1answer
123 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
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0answers
118 views

How can I say that all quantities need to be positive (and real)? [duplicate]

Can you say at the beginning of a script in Mathematica that you want all the quantities to be positive (and real)? So that in all calculations, only the real values of these quantities will be ...
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47 views
2
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2answers
162 views

Nonlinear Optimization with conditional statement

I find Maximize doesn't work well under conditional statement. Here is an example. A car is driving up a slope. I want to find out the largest slope angle the car can drive upwards. I choose the ...
8
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3answers
344 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 ...
4
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1answer
112 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 ...
1
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1answer
81 views

How to obtain dual values? in Simplex(LinearProg.) and… the final tableau? [closed]

I can resolve the function value and the primal values in Linear Programming like in (* Examen de avións Sept 2003 *) ...
9
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1answer
246 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
6
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1answer
361 views

Mathematica vs Sigmaplot (Non LinearModelFit)

I asked a question in a previous post that was closed because "The title of the question is not correct and the issue here is too trivial to help anyone later". NonLinearModelFit It's possible ...
3
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1answer
226 views

How can I set constraints on parameters in NelderMeadMinimize package?

I read about NelderMeadMinimize package. How can I set constraints on the parameters? For example I want to minimize an equation with $10$ parameters such as ${a_1, a_2, ....}$. I want to put the ...
2
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2answers
994 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 ...
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0answers
186 views

FindMaxValue vs FindMaximum

I'm studyng the maximum value of the following function ...
8
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3answers
976 views
1
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1answer
120 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 & & \\ ...
1
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2answers
204 views

What's the best way to generate all the upper triangular matrix whose singular values are given?

For example, given $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what's the best way to generate all the upper triangular matrix ($3\times 3$) whose singular values are $\lambda_i$? Note:Given a ...
2
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1answer
552 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 ...
4
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1answer
147 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 ...
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0answers
107 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 ...
3
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1answer
168 views

Fitting one function to another

I'd like to see how close I can fit an exponential function to a cosine function in the domain of $\;-\frac{\pi}{2}$ to $\frac{\pi}{2}$ in the least squares sense. ...
4
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1answer
988 views

Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
0
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0answers
154 views

How minimize a function involving abs $(|\ldots|)$?

I am trying to decide the best way to solve this: Minimise $Y = | K + ax^2 + bxy + cy^2 |$, with decision variables $x$ and $y$ and $a > 0$. I also have a number of convex and affine ...