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

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Constrained optimization and problem with complex numbers

I am trying to solve a constrained optimization problem with an implicitly defined function $\pi$. The problem is non linear and of high order, so I use numerical methods instead. The code I use is: ...
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0answers
127 views

Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
2
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1answer
131 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
6
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1answer
505 views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
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2answers
264 views

Is it possible to monitor the sum of squared errors in a NonlinearModelFit or FindFit procedure during the process?

Since fitting procedures using NonlinearModelFit (or FindFit) sometimes take very long, I would like to monitor the sum of ...
3
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1answer
107 views

How can I change a lot of parameters to Real? [closed]

Because of some formulas with Conjugate in a notebook, I have to tell mathematica to change a lot of parameters to Real! I know that I can use Refine with Element or Assumptions: ...
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2answers
102 views

Does FindFit use symbolic differentiation?

Does FindFit use symbolic differentiation when optimizing by least squares a non-linear function?
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1answer
146 views

Minimization Nminimize nnum error

I have imported data (mat is the name, 1x100 dimensional vector)and written a likelihood function for normal distribution. ...
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0answers
40 views

Using ForAll in Maximize to define a bunch of conditions [closed]

I'm trying to do something very straight forward. The following maximization works: ...
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1answer
76 views

NMinimize error: Nearest::neard:

I have this function GuessError, here's a plot assuming a single variable x, Plot[GuessError[10^x, etc..], {x, 8, 12}] , being etc some more variables which are ...
2
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1answer
96 views

NMinimize works only if expression is pasted directly

Niminize works fine if I copy the minimized function directly by hands, but doesn't work if I try to do something like this: ...
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1answer
144 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my ...
2
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1answer
70 views

Application of Maximize: The cuboid constrained to the ellipsoid in $\mathbb{R}^3$

Since I am a student of Mathematics I enjoy to apply MMA to problems that I have a solid understanding in. The following would be such a problem: Maximize $f: \mathbb{R}^3 \to \mathbb{R}$ given by ...
3
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1answer
158 views

How to stop optimization (e.g. NMinimize) after reaching target value

Suppose we have some function f[x,y] that we want to optimize in way that we are only interested in values (x,y) that guarantee ...
4
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1answer
102 views

Why does EvaluationMonitor in FindMaximum only work for some regions?

This has come about after trying to understand what was going on with this question about FindMaximum and regions. My first thought in that scenario was to set-up ...
3
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1answer
87 views

Why minimization does not work with symbolic array as arguments

If I try to minimize with constraints a function of several variables, with Gamma regularized function involved in the constraints it seems to works, as shown below (this is just a dummy example ...
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2answers
122 views

Minimize the sum-of-squares errors for a system of ODEs

I'm trying to minimizing the sum of squared errors on a 2-equation system of ODEs and empirical data. I keep getting an error and I think the root of the problem is my invocation of ...
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0answers
115 views

Maximize and NMaximize don't work for my function

I defined the following function: d1[x_] := Min[Abs[FractionalPart[x]], 1 - Abs[FractionalPart[x]]] and tried to evaluate the following function: ...
4
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1answer
123 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...
0
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1answer
150 views

Plotting Minimize output for a range of constraint values

I want to plot the minimum of a function returned by Minimize over a range of constraint values. ...
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1answer
129 views

FindMinimum function does not produce minimum from near point

Using my simple program and I would like to find such matrix elements that minimize difference of their eigenvalues. ...
5
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1answer
288 views

Is there any strategy to have a compiled version of FindFit or NonlinearModelFit?

Disclaimer: This is not a precise question with a definite answer. I know that neither FindFit nor NonlinearModelFit is in the ...
4
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3answers
299 views

How to fit parameters in a system of coupled differential equations

Problem description: I'm studying a chemical reaction that can be modeled by a system of coupled differential equations, and I want to use measured data to determine the parameters that appear in the ...
10
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2answers
2k views

Linear programming with many variables and parameters

I am trying to reconstruct the answer that is given in this report. (page 153 in Appendix B; Section B.2.1). They are given variables, parameters, constraints, and the objective function to minimize. ...
0
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1answer
275 views

Implementing the Golden Section Rule

I am attempting to write a code which brackets the minimum of a unimodal function, using the Golden Section Method Below. I am have serious issues debugging my program though, any help will be ...
43
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7answers
3k views

Character edge finding

The following line of code finds the edge of a character: ...
3
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1answer
430 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 ...
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1answer
93 views

Complicated equation solving

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

Maximise output issue

When I execute the following command, I get a numerical output as follows: ...
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1answer
62 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} + ...
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0answers
135 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 ...
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1answer
91 views

Looping within linear programming

I am trying to do some network programming around optimization. Here is a reduced sample: ...
0
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0answers
88 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 ...
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0answers
175 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
408 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
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 ...
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1answer
106 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 ...
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1answer
111 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
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3answers
913 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
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2answers
130 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
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0answers
113 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
228 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
156 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
165 views

How to implement the dual Lagrange?

I have seen in the Pang book of data mining the following example: ...
0
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1answer
108 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
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1answer
236 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
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2answers
192 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, ...