Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
1,481
questions
1
vote
1answer
501 views
Domain errors with Maximize/NMaximize
I am trying to maximize a (somewhat) complicated function over probability distribution $p$ and $q$. Here is my input:
...
0
votes
1answer
178 views
Maximization of a function within a unit square [closed]
I work in a unit square. I have some conditions under which areas within the unit square are defined. Say for simplicity that there are two conditions which define two areas. For example, if y > 1/2 ...
1
vote
1answer
867 views
Numerical saddle point problem of a function of many variables
I want to find the following saddle point of the function of 10 variables:
.
I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
1
vote
1answer
1k views
Symbolic Constrained Optimization
I have a question regarding evaluating constrained optimization problems in symbolic terms. I would like to perform How can I implement the method of Lagrange multipliers to find constrained extrema? ...
3
votes
1answer
942 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). ...
1
vote
1answer
99 views
2
votes
1answer
1k views
Finding exact local extrema of simple functions
I want to exactly find all the local maxima of
f[x_] := x^4/4 - x^2/2
over the interval [-Sqrt[2], 1 + Pi/10].
The correct ...
2
votes
0answers
261 views
Combination of linear programming with bilevel optimization
I'm not a programmer really (interested in mathematics actually). Excuse me if I can not coding good. I'm also interested in implementation of mathematics results in programming language. That's my ...
2
votes
1answer
192 views
NMaximize and Accuracy
I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
3
votes
2answers
577 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 ...
7
votes
1answer
319 views
Large scale linear programming (Data imported from .mat file)
I tried to run a large scale linear programming with mathematica.
I entered the code below:
...
3
votes
1answer
207 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 ...
4
votes
1answer
502 views
$L_\infty$ norm minimization
I write supplemental explanation to render my aim of optimization.
First Consider discrete time linear system below:
\begin{equation} G(z)=\frac{1-e^{-0.3T}}{z^{100}(z-e^{-0.3T})} \end{equation}
...
1
vote
1answer
879 views
How to perform a symbolic minimization?
Can Mathematica determine the symbolic expression in terms of Ļ that minimizes f[Ļ] ?
...
26
votes
2answers
2k views
Schedule programing problem with integer linear programming
I know how to model this question on paper, but I don't know how doing it in Mathematica.
Imagine , there is a university student who want to choose courses for this semester and he got the ...
0
votes
0answers
66 views
Compiling Visual Studio C++ to Run on Computers without Mathematica [duplicate]
I have written a console application on Visual Studio C++ as below
...
10
votes
3answers
1k views
How can I complete a correlation matrix with missing values?
I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
12
votes
1answer
1k views
Fitting Vogel's formula for phyllotaxis to the image of a flower
After having read this question I was inspired to investigate how we could take an image of a plant displaying phyllotaxis and fit Vogel's model of phyllotaxis to the image. The theory is very simple.
...
2
votes
1answer
169 views
Declaration of variables in large Linear Programming model with NMaximize
I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem:
$$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\
s.t\quad
\...
3
votes
1answer
201 views
Decomposing a diagonal positive real matrix
I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$:
$$E = \left(
\begin{array}{ccc}
0 & & & \\
& a & & \\
&...
6
votes
0answers
205 views
Issue with FindCurvePath
I have a problem with the function FindCurvePath. In some cases it crashes the Mathematica 9 Kernel. Here an example, where it crashes the kernel:
...
1
vote
1answer
290 views
NMinimize stops with no more memory?
I am using NMinimize function for simulation based optimization. So my objective function is a simulation that runs for every combination of variable values evaluated by NMinimize function. However, ...
4
votes
1answer
864 views
Arnold's problem #8
The famous Arnold's problems (see
http://www.math.upenn.edu/Arnold/Arnold-Trivium-1991.pdf ) are
aimed at the strong graduate and postgraduate students of the top universities.
I find it remarkable ...
28
votes
2answers
6k views
Optimization of a portfolio of stocks
I would like to use Mathematica to perform an optimization of a portfolio composed by 10 stocks. I did the first part to compute yields and expected yields, but I don't know how to finish the ...
4
votes
1answer
605 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 ...
3
votes
0answers
508 views
Minimizing a functional takes forever
I need help with minimizing a functional in Mathematica.
I have a function $V(\xi)=\sum_{i=1}^\infty C_{3_i}J_0(\xi/C_i)+C_{4_i}Y_0(\xi/C_i),~~~\Sigma\leq\xi\leq\xi_1$, and want to find such $\{C_{...
5
votes
1answer
1k 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.
...
-1
votes
3answers
6k views
How do I determine the maximum value for a polynomial, given a range of x values?
I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
2
votes
1answer
649 views
Why is `NMinimize` trying to evaluate my function analytically instead of numerically?
I have been having some trouble with NMinimize. I am trying
NMinimize[f[x], x]
where f is ...
5
votes
2answers
202 views
Finding the maximal `t` at which `u[x,t] == 1`?
Given the smooth function u[x,t] on a domain, how do I find the maximal t at which ...
4
votes
1answer
658 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 ...
2
votes
1answer
1k views
FindMinimum produces error message
I'm trying to solve a logistic regression problem using Mathematica -- more to improve my Mathematica skills than to solve the problem as I have already solved it using Octave.
The problem I am ...
20
votes
3answers
9k views
How can I implement the method of Lagrange multipliers to find constrained extrema?
I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
3
votes
0answers
334 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
1answer
710 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 ...
7
votes
2answers
221 views
How to Maximize[Log[n]^(1/Log[n]), n]
I am new to Mathematica and am trying to work out how to use Maximize.
Maximize[Log[n]^(1/Log[n]),n]
Should give a solution at $e^e$. However in Mathematica you ...
13
votes
1answer
3k views
Which methods are available for NMinimize?
I can't find in the documentation the list of methods available to NMinimize[]. Is there a way to get this?
The NMinimize page in Documentation Center mentions only ...
4
votes
1answer
2k views
1
vote
1answer
192 views
Bound on number of function evalulations in FindMinimum
I am minimizing a nonlinear constrained problem using FindMinimum. The problem involves about 200 variables and the function is a black-box which cannot be compiled/...
4
votes
1answer
284 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 ...
2
votes
1answer
163 views
LinearProgramming errors
I have a family of equations I want to solve over the non-negative integers. One particular instance of it is this.
...
4
votes
0answers
291 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 ...
7
votes
1answer
552 views
2
votes
1answer
1k views
Simulated Annealing InitialPoints option
I have a cost function that depends on 4 parameters: CostFunction[{tx,ty,tz,ox}].
I used NMinimize[] function with ...
1
vote
1answer
605 views
No Speedup Compiled Function in FindMinimum
The problem: I would like to minimize an objective function with respect to 12 variables. Minimization should be executed as fast as possible. Compiling the objective function increases the execution ...
2
votes
1answer
2k views
FindMinimum [] methods [closed]
Which algorithm is used when we do not use the option Method of FindMinimum[] function.
FindMinimum[f,{x,x0}]
0
votes
0answers
53 views
How to manipulate lists to get only part of the value [duplicate]
This is really a question about manipulating the output of Maximize. I have a function of 2 variables, defined thus:
...
1
vote
1answer
172 views
2
votes
2answers
320 views
Nonlinear Optimization with conditional statement
I find Maximize doesn't work well under conditional statement. Here is an example.
A car is driving up a slope. I want to find out the largest slope angle the car can drive upwards. I choose the ...
10
votes
4answers
983 views
Finding a point from a set of contours such that it is nearest to a given point
I have several contour lines and one point. How can I find a point in one of those contour lines which is nearest to the given point?
...
