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

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1
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2answers
167 views

Minimizing the largest difference between two functions

I have two functions defined on the same domain, $f(x)$ and $g(x)$ where $x$ is in $(0,1)$: f[x_] := (-1 + x) Log[1 - x] - x Log[x] g[x_] := Log[1 + 2 (-1 + x) x] ...
0
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2answers
64 views

Vector optimization with vector length as a free variable

I'm trying to solve the following problem: For a vector $v$ of length $c$, $\min \frac{\sum v[i]^4}{(\sum v[i]^2)^2}$ subject to $\sum v[i] = N$. I can solve this numerically for a given $c$ using ...
1
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1answer
77 views

Optimizing matrix inequalities over trace

I need to solve the following problem. Given $n \times n$ Hermitian matrices $A\geq 0$ and $B_1, ~ B_2$ (need not be positive semidefinite), with $Tr(AB_1)<0~,Tr(AB_2)<0$ construct a ...
0
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0answers
32 views

FindMaximum slow for fixed parameters

I hope my problem can be solved by just showing you this tiny part of my code which does not run on its own. I have an optimization problem and want these functions to work on various data sets. ...
0
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0answers
40 views

Parallelize: No speed-up when using with FindMaximum

I have developed a program to compute the maximum value of an specific function multiple times, with different parameter values each time. I've been using the ...
1
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1answer
55 views

Precision of starting values in FindMinimum [closed]

I am currently working on an optimization of chemical kinetic model. Starting points for FindMinimum are defined as: ...
7
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3answers
690 views

Built-ins for discrete ArgMax or ArgMin?

Wondering whether there are discrete versions of ArgMax / ArgMin, that is, something that will find the part of an expression at ...
2
votes
2answers
103 views

Only one root at specific interval

I need a help to find k here: $f(x)=-k^x + x^2$ It is not too simple. I have interest to find the single value of "k" where, inside interval {x,2,3}, the function have only one value to x when f(x) ...
50
votes
4answers
11k 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 ...
24
votes
4answers
5k views

Finding Local Minima / Maxima in Noisy Data

I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
0
votes
0answers
61 views

Mathematica global optimization add ons

Can somebody tell me the major differences between Global Optimization add on, MathOptimizer Professional, and NMinimize which does global optimization in ...
0
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0answers
89 views

How to find Multiple Maxima/Minima

I am trying to solve a problem that requires finding multiple maxima of a numerical function. So the function generates some numbers that are coming out of an experiment. I tried using NMaximize or ...
3
votes
2answers
93 views

Finding large Collatz Sequences, trying to improve speed

Background: I am already very much in love with Mathematica but I am also a novice. So far I have only gathered experience in procedural programming in Python. Generally speaking I am trying to ...
2
votes
1answer
91 views

Simple-looking Minimize takes for ever

Consider the following: Minimize[{(ξ - x)^2 + (η - y)^2, a ξ + b η == c}, {ξ, η}, Reals] After asking Mathematica to do this yesterday afternoon and forgetting ...
2
votes
1answer
135 views

How to implement the dual Lagrange?

I have seen in the Pang book of data mining the following example: ...
0
votes
1answer
65 views

Optimizing complex functions

I am trying to optimize a function containing complex numbers, however I keep running into errors. Consider the simple optimization problem: ...
0
votes
1answer
69 views

Incorporate error bars to best-fit curve [closed]

I have managed to get mathematica to perform a best fit curve. However, I wish to add error bar to the curve, how do I do so?
0
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0answers
15 views

NMinimize as objective function of NMinimize [duplicate]

Let f[x_,z_]:=... g[x_,z_]:=... fully numerical apart for x and z. Then, I want to find z by minimizing f^2 for given x. Then, I want to find x that maximize g for z in the first step (which is a ...
1
vote
2answers
181 views

How do I disorder a list in Mathematica?

Given a list like this (the original list is much longer), how I can get a completely unordered list and save it in plain text? I change the file names (names at random), using a length of 5 digits, ...
0
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0answers
44 views

Some of System words in Mathematica 10 doesn't show right

Does anyone have any idea about why this happens and how to solve it? thanks.
2
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0answers
37 views

Where can I find detailed information about the SystemOptions?

I'm looking to optimize my Mathematica script, and I'm willing to go spelunking with low-level system options. The problem is that I've been looking in the Mathematica documentation, but there ...
4
votes
1answer
74 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
0
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0answers
35 views

Convex problem solution

I have the following optimisation problem, where $l,m,n$ are positive. It is a convex problem. I need to find the optimum under a budget constraint. ...
0
votes
0answers
143 views

Is there a way to give Mathematica extra memory?

I am running Mathematica 10 (Student Edition) on Mac OS X 10.7.5 on an old Mac Pro. I have lots of extra RAM that the system isn't touching, and I would like to give some of it to Mathematica in the ...
5
votes
1answer
127 views

Slow-down encountered when using NMinimize with a compiled function

I'm minimizing a large function. Evaluating the function is very slow symbolically but using Compile I can get ~100x speed-up on this step. However, despite this, the NMinimize process is only ...
0
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0answers
77 views

How to properly pass function as argument here? --> NMinimize & NIntegrate involved

I had a problem of a similar kind here which was solved. Now after changing a few things in my problem setting I am suffering from the following problem. Let me first introduce methods/functions that ...
1
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1answer
91 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
0
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0answers
57 views

Fit a complicated function to a constant with NonlinearModelFit

I wish to fit a complicated parametric function (logder, with lambda parameters) to a constant (L) in order to minimize its dependence with the variable k in a given interval. To do that, I use a ...
6
votes
1answer
243 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are ...
1
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1answer
48 views

Getting result from Maximize

I'm trying to get maximization result from Maximize function to use it in later calculations. At the moment I use the following code: ...
0
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0answers
32 views

Variables input generation for Minimization in High dimensional space

I'm currently doing optimization in a high dimensional space. I was thinking of giving FindMinimum (or NMinimize not certain ...
0
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0answers
30 views

How to evaluate NMinimize inside a function

I want to define a function that returns a sum of differences of some points to a given function. To obtain these differences I would like to use NMinimize, but if I implement that straightforwardly, ...
0
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0answers
32 views

Tricks to speeding up optimisation of a function involving a heavy integration

This is the code, and energycoeffs[] is the function that takes in a dxd matrix and spits out a scalar value. ...
1
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2answers
163 views

Problem with FindMinimum

I am struggling with a problem on fitting a function to my data using FindMinimum. The problem is related to small angle x-ray scattering and my approach is the following: I define the electron ...
1
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1answer
115 views

Using FindMinimum with matrix input

I define the following function which spits out a number S when I feed it a dxd square matrix: ...
1
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0answers
109 views

NMaximize with matrix input

I defined function f[x_, fixed_] := {...}. Here x is an $M\times N$ matrix. I want to maximize $f$ with respect to $x$. I have ...
0
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0answers
72 views

Problem with the laplace transform

I am trying to write a program in mathematica to solve green's functions, like the following. They come up all the time in Quantum Field Theory. I have learned, student's can sometimes see it better ...
0
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0answers
25 views

Iterating a model with 2nd order difference equations using Manipulate [duplicate]

I have a model including first and second order difference equations. It works for the case of first difference equation, which is below: ...
1
vote
2answers
101 views

optimization of CountourPlot with NIntegrate

I have to use ContourPlot with a complicated function depending on 2 parametrs (that I cannot report here) that contains numerical integrations. Here is a simple ...
4
votes
2answers
85 views

NMinimize in one-dimensional Interval

An Interval should be a one-dimensional region, so a region. I tried to minimize a function over an interval, e.g.: ...
1
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0answers
106 views

How to plot feasible objective space of a Generic Multiobjective Optimization problem?

As you know, a generic Multiobjective optimization problem can be stated as follows: $min{\space}F(\bf{X})=[f_1(x),...,f_n(x)]$ $h_k(x)=0{\space\space\space} k=1,...,n_e$ ...
20
votes
1answer
564 views

Convex optimization

I am playing with some Compressed Sensing (think single pixel camera) applications and would like to have a Mathematica equivalent of a Matlab package call Convex Optimization (CVX). Specifically, I ...
4
votes
0answers
90 views

Packages for Semidefinite programming

This question has already been asked here. I am not sure, whether I should have asked this question as a comment of an old question or in the general programming forum of stackexchange. Moderators ...
-1
votes
1answer
67 views

Black Ovals appeared in my Mathematica notebook [duplicate]

I copied and pasted something from another Mathematic notebook and started getting the same black ovals seen in this question: Colored marks appearing in notebook input text? The suggestion to turn ...
4
votes
0answers
162 views

How to determine reason for kernel crash? -> Nelder Mead optimisation

I am making use of the Nelder Mead algorithm inside Mathematica's NMaximize to find a parameter set by solving the Schrodinger equation for a given system. (see ...
0
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0answers
51 views

Minimize doesn't solve a problem with many symbols

I am trying to solve a simple constrained optimization problem. I am running the code ...
1
vote
2answers
77 views

Maximum likelihood estimation based on frequency table

I have a frequency table of grades, I'm trying to estimate the distribution as a truncated normal distribution (a grade below 65 is a failing grade and doesn't count). Since I don't have the actual ...
0
votes
0answers
102 views

Nash equilibrium in game theory?

Are there examples of the solution of Nash non-cooperative games with mixed or pure strategies? How could be implemented in Mathematica 10?