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

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43
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
3
votes
1answer
426 views

FindMaximum of loglikelihood in Gaussian Process

I am trying to implement a Gaussian Process and have problems to maximize the loglikelihood because the function consists of a determinant of a matrix that is dependent of 2 variables and the product ...
1
vote
1answer
93 views

Complicated equation solving

I want to find the maximum point or optimal value $y$ of Rx1[y_, a_, b_]. ...
6
votes
2answers
83 views

Maximise output issue

When I execute the following command, I get a numerical output as follows: ...
0
votes
1answer
59 views

Minimizing a function which involves Maximize [duplicate]

I have a mathematical function: $f = \frac{c^3}{2 a (k T)^3} \sqrt{\frac{\pi u v w}{2 b}} \exp \left[ - \frac{c}{k T} \sqrt{\frac{x^2+y^2}{a}+\frac{z^2}{b}} + \frac{1}{2} \left( \frac{x^2}{u} + ...
1
vote
0answers
134 views

How can I speed up this NM optimization? Most delay seems to be due to long analytic expression

I am struggling with computational speed of a NelderMead optimization. Nevertheless my impression is that I lose lots of speed not only due to the NM optimization itself but rather to for instance ...
-1
votes
1answer
91 views

Looping within linear programming

I am trying to do some network programming around optimization. Here is a reduced sample: ...
0
votes
0answers
83 views

imaginary part in optimization problems

I have some trouble with an optimization problem. The constraints are always real, but in the first place there are also complex parts in the expression (which all sum up to 0). The problem now is ...
1
vote
0answers
169 views

Imposing constraints to NMinimize/NMaximize leads to wrong function values

I wrote a function that uses NMaximize to find certain parameters (using NelderMead simplex algorithm). My objective functional $J({x_i})$ is real-valued and its ...
1
vote
2answers
401 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
votes
2answers
78 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
vote
1answer
104 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
votes
0answers
77 views

Parallelize: No speed-up when using with FindMaximum [closed]

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
vote
1answer
105 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: ...
8
votes
3answers
899 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
129 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) ...
0
votes
0answers
111 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
votes
0answers
227 views

How to find Multiple Maxima/Minima [duplicate]

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 ...
2
votes
1answer
153 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
163 views

How to implement the dual Lagrange?

I have seen in the Pang book of data mining the following example: ...
0
votes
1answer
104 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
226 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?
1
vote
2answers
191 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, ...
2
votes
0answers
49 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 ...
5
votes
1answer
159 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
5
votes
1answer
262 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 ...
1
vote
1answer
100 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
votes
0answers
103 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 ...
7
votes
1answer
400 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
vote
1answer
77 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
votes
0answers
38 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, ...
1
vote
2answers
204 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
vote
1answer
141 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
vote
0answers
119 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
votes
0answers
129 views

Problem with the laplace transform [closed]

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
votes
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
122 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 ...
5
votes
2answers
144 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.: ...
2
votes
0answers
189 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: $min{\space}F(\bf{X})=[f_1(x),...,f_n(x)]$ $h_k(x)=0{\space\space\space} k=1,...,n_e$ ...
23
votes
1answer
826 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 ...
5
votes
0answers
268 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
96 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 ...
6
votes
0answers
237 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 ...
1
vote
2answers
119 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 ...
1
vote
0answers
176 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?
-1
votes
1answer
78 views

My code of plotting a two-variable function is too slow [closed]

I have a code in which my complicated function to be plotted is F(x,p). I would like to graph it for 5 values of p equal to 10^7, 10^8, 10^9, 10^10 and 10^11 for x values between 0.01 and 0.99. All ...
1
vote
1answer
179 views

How to properly apply NumericQ or s.th. similar here? - NDSolve inside NMaximize

I wrote a function that numerically solves a given Schrodinger equation and returns replacement rules to obtain the time evolution operator. It looks and is used as follows: ...
2
votes
1answer
216 views

How to find Lagrange multipliers corresponding to constraints?

I have a constrained optimisation problem that I solved using Mathematica's FindMinimum function. I would like to know how to get the dual variables corresponding to the constraints I have. Obviously ...