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

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4
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1answer
219 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 ...
1
vote
3answers
208 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): ...
3
votes
2answers
276 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 ...
2
votes
1answer
502 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 ...
3
votes
1answer
457 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: ...
3
votes
1answer
376 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, ...
34
votes
3answers
2k 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 ...
9
votes
4answers
286 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. ...
1
vote
2answers
2k 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 ...
3
votes
1answer
321 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 ...
4
votes
0answers
409 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?
2
votes
0answers
284 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. ...
2
votes
2answers
895 views

optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
2
votes
1answer
671 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: ...
5
votes
2answers
402 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 $A[0]$. ...
0
votes
0answers
83 views

How to Clear a symbol with subscript in Mathematica? [duplicate]

Possible Duplicate: Clear complains that a variable is not a symbol or a string? I want to clear $\lambda_0$ which is assigned to be $\lambda_0=1$. From the reference here, Clear ...
19
votes
2answers
765 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 ...
4
votes
1answer
628 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: ...
6
votes
1answer
282 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 ...
4
votes
1answer
210 views

Assumptions seem not to be considered

In the following a,b is a probability distribution, i.e. a+b==1 with ...
45
votes
4answers
9k 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 ...
6
votes
1answer
396 views

Defining a non-linear optimization-problem

Consider the following non-linear optimisation problem: ...
58
votes
2answers
4k 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
votes
3answers
385 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 ...
11
votes
2answers
1k 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
votes
4answers
3k 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 ...
8
votes
1answer
2k views

Solve Lagrange multipliers optimization problem

I have two nested solid figure, where $V(a,h,\tau)$ defines the volume and $A(a,h,t)$ defines the surface. The outer solid figure is parametrized in $a_s$,$h_s$ and $t_s$ (they share a common center). ...
17
votes
2answers
663 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
4
votes
1answer
191 views

Why is this minimization with Boole functions failing?

I am running this command in Mathematica 8.0.4.0: ...
0
votes
1answer
355 views

Symbolic Optimisation

I'm trying to solve symbolically the following optimisation: $$ \min_{q_uu}\ \Biggl[ q_u q_{uu}\psi B_{uu} + q_u q_{ud}\psi B_{ud} + q_d q_{du}\psi B_{ud} + q_d q_{dd}\psi B_{dd} $$ $$ + ...
12
votes
2answers
617 views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
7
votes
1answer
644 views

Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations

The formal problem The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
35
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
13
votes
3answers
854 views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
10
votes
1answer
1k views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...