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
165 views

Minimize failing on a polynomial

Calling: Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2, 0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}] returns ...
4
votes
1answer
342 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - ...
4
votes
1answer
220 views

Assumptions seem not to be considered

In the following a,b is a probability distribution, i.e. a+b==1 with ...
4
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1answer
216 views

Ordinary differential equation invloving the function composition

I want to solve the following function: DSolve[(A1*Exp[B1*f[x]] + A2*Exp[B2*f[x]])*f'[x] == A1*Exp[B1*x] + A2*Exp[B2*x], f[x], x] And this is what I get as an ...
4
votes
1answer
139 views

Forcing optimal solution for FindShortestTour

I use FindShortestTour as explained here and it works nicely for a small number of cities. However when I try this with as little as 16 cities, the given tour isn't ...
4
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1answer
53 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 ...
4
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1answer
105 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 ...
4
votes
2answers
73 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.: ...
4
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0answers
75 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 ...
4
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0answers
152 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 ...
4
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0answers
176 views

Simulated Annealing Parameters and Results

I am using SimulatedAnnealing method for a simulation based optimization problem and was wondering if someone can enlighten me on the following features: Is there ...
4
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0answers
216 views

Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem) [duplicate]

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
4
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0answers
567 views

When using NMinimize[…,Method->“DifferentialEvolution”] is an “iteration” different than a “step”?

Hopefully this question has a simple answer. I have the following bit of code: ...
3
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2answers
697 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
3
votes
2answers
255 views

NMinimize/NMaximize is unable to generate initial points

Mathematica 10 generates a warning that it is unable to generate initial points for numerical optimization problems. I picked a particularly simple example. The problem goes away when ...
3
votes
3answers
175 views

How to shade a plotted region in specific direction?

I am using RegionPlot to plot a linear program maximize 30x1+25x2 with the constraints ...
3
votes
1answer
413 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, ...
3
votes
1answer
154 views

Finding peaks of data

I want to find peaks in my data. My code in a reduced form so far: ...
3
votes
1answer
112 views

What does LinearModelFit depend on except for its' arguments?

I thought this would be always true, but most likely it returns false. ...
3
votes
3answers
266 views

Fastest way to check if an expression contains all symbols from a list

I need to execute this function thousands of times, and the faster, the better. I came up with two versions, but wanted to see if you can come up with an even faster way. Is there a better way? I use ...
3
votes
1answer
318 views

Fitting one function to another

I'd like to see how close I can fit an exponential function to a cosine function in the domain of $\;-\frac{\pi}{2}$ to $\frac{\pi}{2}$ in the least squares sense. ...
3
votes
2answers
422 views

Optimization problem with matrix positivity constraints

Is it possible for Mathematica to parametrically find a local minimum of a given function (say of some variable $x$ where $(a,b,c)$ serve as parameters) subject to the constraint that a given ...
3
votes
2answers
286 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 ...
3
votes
1answer
120 views

Calculate the relationship between the duration of two oscillating functions

I am trying to quantitatively determine the relationship between the length of two oscillating functions. Meaning, what is the duration of the green spike in relation to the blue square? Does anyone ...
3
votes
2answers
444 views

Convert number to exponent form with highest power possible

As a school assignment we have to write a program which solves this issue. Since the program has to run efficient I am wondering what the best way is to approach this issue. Of course there you can ...
3
votes
1answer
312 views

How can I set constraints on parameters in NelderMeadMinimize package?

I read about NelderMeadMinimize package. How can I set constraints on the parameters? For example I want to minimize an equation with $10$ parameters such as ${a_1, a_2, ....}$. I want to put the ...
3
votes
3answers
71 views

Minimizing Multiple Functions

I'm trying to write a script that will minimize a given set of functions. The homework problem I've been given lists a set of dietary information, and I'm supposed to build the optimal salad based on ...
3
votes
1answer
192 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions of ...
3
votes
1answer
353 views

Find Chebyshev center of a region by optimization

Let's consider a region like this: The aim is to find the "Chebyshev center" of the region. By using the polygons, one can approximate the perimeter of region by an $n$-gon ($n$ is large enough). ...
3
votes
1answer
477 views

FindMinimum, NMinimize, etc. with external process

I was hoping to be able to use MMA's minimization power to work with an external process. I want to minimize the function 'TryThisNumber[x_]' which sends the value of x to something external and gets ...
3
votes
1answer
95 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 ...
3
votes
1answer
268 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 ...
3
votes
1answer
566 views

How to maximize a function over a rotation matrix?

I have list of pairs of points: $\{(x_i,y_i)\}_{1\le i\le n}$, $x_i \in \mathbb{R}^3$, $y_i \in\mathbb{R}^2$ and would like to optimize over a rotation $R \in SO(3)$, a translation $t \in ...
3
votes
2answers
355 views

Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
3
votes
1answer
200 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
3
votes
1answer
536 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
65 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 ...
3
votes
1answer
86 views

Bug with LinearProgramming on Integers?

With Mathematica 7: LinearProgramming[{1, 1}, {{0, 0}, {1, 1}}, {1, 1}, Automatic, Integers] gives wrong result {0,1}. But ...
3
votes
2answers
142 views

Find condition under which variables fall away

I have a somewhat lengthy expression, looking like expr = 1 + x + b + Pi + 2*a Is there some way of generating a relationship between ...
3
votes
1answer
707 views

How to use mathematica to create school time-table?

I wonder if it is possible to use Mathematica for helping myself to create school timetable. I have a feeling that it requires quite simple optimization algorithm, but I have never been into ...
3
votes
1answer
154 views

Mathematica Library

I created a Mathematica packagr and then I used the Needs function to add the library to my .nb file, but when use a function in my .nb file and the function is built in my library it comes up with ...
3
votes
1answer
91 views

quadratic constraint feasibility

Suppose that $A$ is an $n \times n$ matrix, and I have observed some entries of $A$, say, $A_S$ ($A$ restricted on $S$) for some subset $S$ in $\{1,...,n\} \times \{1,...,n\}$. I want to know if it's ...
3
votes
1answer
340 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 ...
3
votes
0answers
48 views

How to perform Bayesian optimization with Mathematica?

Does Mathematica have any Bayesian optimization methods for learning hyper-parameters? Practical Bayesian Optimization of Machine Learning Algorithms Jasper Snoek, Hugo Larochelle and Ryan P. ...
3
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0answers
63 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code that uses NonLinearModelFit with NMinimize as the method to do ...
3
votes
0answers
78 views

Efficient processing of Special Ordered Sets with LinearProgramming

I'm playing with integer linear programming, especially problems involving lots of constraints which would appear to be special ordered sets. Below is a toy example, three last rows of the matrix ...
3
votes
0answers
221 views

Optimization with Matrix value constraint

I am trying to find the orientation and position of a polygon resting on a curved surface under gravity.The polygon MUST not be penetrated by any part of the surface below. Here is an example for a ...
3
votes
0answers
175 views

Trouble with Minimize

Minimize[{t^2, 1 == 3*t + 16*u}, {t, u}, Integers] It does not give the solution t = -5 and u = 1. Am I missing something? The solution being known and ...
2
votes
2answers
1k 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
2answers
394 views

Maximum of Minimum of a two variable function

I have F[x, y] := (y/2)(2 Cos[2x] + 2 Cos[x] + 1)/5 + ((1 - y)/2)(2 Cos[x] + 1)/3. I am looking for the maximum of the minimum of ...