Questions tagged [mathematical-optimization]

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

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149 views

How to express this output in the form $X=A.x$?

This problem arose in my stereo vision project. I have two matrices: $$ A = \left( \begin{array}{ccc} \text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & \text{x1}*\text{...
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1answer
188 views

Seemingly simple optimization problem is slow

I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so: ...
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1answer
617 views

How can I fit a matrix function with multiple variables to given eigenvalues?

I have a 5x5 matrix function H[kx] ...
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1answer
477 views

Finding resolution of an optical system using Rayleigh criterion

I want to use the Rayleigh criterion to find the resolution of an optical system. I have two functions f1 = Sinc[x]^2 and ...
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1answer
815 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
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0answers
83 views

Using lists as optimization parameters [duplicate]

Possible Duplicate: Minimizing a function of many coordinates Suppose that the function $F[\vec{x}]$ computes a certain polynomial of the elements of the list $\vec{x}$. How can I use ...
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1answer
416 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
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0answers
663 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
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2answers
956 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, <...
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1answer
1k views

Restrictions problem

I tried to program a simple linear optimization model and don't know where my mistake lies. The function should be a sum over "t" and "z" from the product of two constants ("e" and "H") and the ...
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3answers
4k views

Determining the local extrema of discrete data [duplicate]

Possible Duplicate: Local max/min of Mathematica data sets If I have a continuous function f (for example f = Sin[x]), I ...
4
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1answer
411 views

Maximizing functions with Which statements

I'd like to be able to find the maximum value that my Capex function (see below) generates. This is a fairly simple function so I could just add it up but I have more complex functions of a similar ...
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1answer
2k views

How to find local minima of a multivariate function with singularity?

I am working on a logistic regression problem which requires minimizing a cost function J[{theta0, theta1, theta2}, X, y] to find the optimal value for fitting ...
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1answer
536 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
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2answers
1k views

How can I speed up the classic GA for graph coloring?

I'm trying to compute the chromatic number of this graph (which is 28): g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col"; My genetic ...
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1answer
2k views

FindMaxValue and FindMaximum - how to find GLOBAL maximum and not just LOCAL maximum

I will not be able to provide a simple minimum working example here as this seems to be very specific. I have an interpolating function which I substituted into a PDE and then plot said PDE at a ...
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1answer
2k views

How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
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1answer
383 views

Different results for MaximumLikelihood depending on method?

When I used this command: ...
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2answers
1k views
3
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1answer
1k views

How to use mathematica to create school time-table?

I wonder if it is possible to use Mathematica for helping myself to create school timetable. I have a feeling that it requires quite simple optimization algorithm, but I have never been into ...
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2answers
199 views

Scalar product of two vectors have the least value

In geometry 3D, let $A(1,2,-3) $ and $B(-1,4,1)$ are two points. In the plane $(P):2x-3y+3z-17=0$, find a point $M$ such that the scalar product of two vectors $AM$ and $BM$ will have the least value. ...
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1answer
2k views

Multi-objective genetic algorithm in Mathematica?

Is there any implementation of a multi-objective genetic algorithm for Mathematica?
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2answers
2k views

Implementation of a new Game of Life Rule

I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action. I would like to implement the ...
4
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1answer
839 views

FindMinimum, NMinimize, etc. with external process [duplicate]

I was hoping to be able to use MMA's minimization power to work with an external process. I want to minimize the function 'TryThisNumber[x_]' which sends the value of x to something external and gets ...
5
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1answer
316 views

Optimizing a rank 3 tensor

Assume we have the following elements \begin{equation} F_i{}^j \;and\; S_{ij}{}^k, \end{equation} which represent the components of tensorial objects of ranks 2 and 3 respectively, with Complex ...
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3answers
328 views

How to find maximum ConditionalExpression among all solutions

For example I want to find solution with maximum value among solutions (and possibly plot it): ...
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2answers
374 views

Find all points that have the same minimum? [duplicate]

Possible Duplicate: How to find all the local minima/maxima in a range Sin[x] have two points ($3\pi/2,7\pi/2$) where the same minimum ($-1$) is achieved at ...
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1answer
854 views

Problems with FindMinimum for Constrained Optimization

I am trying to define a simple optimization problem, arising from the discretization of a simple Optimal Control problem. The problem that results is essentially linear, with bilinearities only ...
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1answer
1k views

wrong use of _?NumberQ?

I am having trouble with a numerical exercise. Here's a simplified version of my problem. I define two functions to find the solution to two constrained maximization problems: ...
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1answer
543 views

Handing a list of constraint expressions to a C++ function with MathLink

I need to solve an optimization problem, which is defined in a Mathematica notebook. Using Mathematica's FindMinimum is not an option, because it is too slow. So, ...
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3answers
4k views

Identifying critical points/lines of 2/3D image/cubes

Upshot I am interested in identifying critical points of a 3D field/cubes (maxima, minima, tube-like and wall-like saddle points) and 2D field/image (maxima, minima, saddle points). I.e. the ...
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4answers
465 views

How can I efficiently check if a graph is unit distance?

A unit distance graph is a graph that is embeddable in the plane so that every edge has length 1. ...
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3answers
2k views

How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
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2answers
4k views

Find the dimensions of a cylindrical can that will minimize the cost of the material

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. This is a standard calculus problem. The volume of the ...
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1answer
506 views

parameter optimization

Does anybody know of any tutorial material that explains how to use Mathematica to fit parameter values used in a set of ordinary differential equations to experimental values stored in a comma ...
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1answer
1k views

Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
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0answers
316 views

Having difficulty with the Minimize command

I am having trouble getting an answer to this question...Am I missing something that anybody can see. ...
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2answers
2k views

optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
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1answer
1k views

Optimizing a function involving NDSolve results in error messages

I want to minimize a function f with NMinimize but an error occurs that says: ...
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2answers
716 views

What alternative notation of subscripts/superscripts that are also treated as SYMBOLS in Mathematica?

I tried to avoid using the subscript $A_0$ in the Module, and get an error with $A[0]$. ...
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2answers
2k views

Optimization with assumptions

I have the following problem, when I am trying to optimize function with pre-defined assumptions. I am using Mathematica 8 and I wrote the following simple code ...
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1answer
1k views

How to solve a quadratic integer programming problem?

I want to solve a quadratic integer programming problem in Mathematica. My first attempt looks like this: ...
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1answer
349 views

Numerical problems with calculation of function

I have a problem with a calculation which I try to do with Mathematica (8.0.1). I have the following function which describes a cone (with half opening angle theta)...
4
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1answer
296 views

Assumptions seem not to be considered

In the following a,b is a probability distribution, i.e. a+b==1 with ...
70
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5answers
22k views

How to find all the local minima/maxima in a range

I want to find : all local maxima in range all local minima in range From those points I can interpolate and combine functions upper and lower boundary. What I am really interested in, is the mean ...
6
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1answer
513 views

Defining a non-linear optimization-problem

Consider the following non-linear optimisation problem: ...
88
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2answers
7k views

Shaving the last 50 ms off NMinimize

The epilogue: A paper where the below answer is used was published. The answer below is cited among the references:) The background: I have to fit an objective function for ~10 000 datasets in near ...
9
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3answers
518 views

Strange domain dependency with Maximize

I'm using Mathematica 8 and strangely enough this code: Maximize[{x*(1-0.01 x),x>0},x,Integers] produces the result ...
12
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2answers
3k views

Maximizing a function with assumptions

Using f[s_] := Log[(s/r)^α ((α - 2) n0 r^α + 2 π Pmax ρ r^2) /((α - 2) n0 s^α + 2 π Pmax ρ s^2)]/s When I run the following line: ...
12
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4answers
6k views

Minimizing a function of many coordinates

I'm trying to obtain a series of points on the unit sphere with a somewhat homogeneous distribution, by minimizing a function depending on distances (I took $\exp(-d)$). My points are represented by ...