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

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56
votes
2answers
3k 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
346 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 ...
10
votes
2answers
833 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). ...
15
votes
1answer
459 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
185 views

Why is this minimization with Boole functions failing?

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

Symbolic Optimisation

I'm trying to solve symbolically the following optimisation: $$ \min_{q_uu}\ \Biggl[ q_u q_{uu}\psi B_{uu} + q_u q_{ud}\psi B_{ud} + q_d q_{du}\psi B_{ud} + q_d q_{dd}\psi B_{dd} $$ $$ + ...
11
votes
2answers
557 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
533 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 ...
32
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
13
votes
3answers
758 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: ...