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

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2
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0answers
187 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
12
votes
2answers
651 views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
4
votes
0answers
501 views
2
votes
1answer
193 views

How can I change the MPS format in Linear Programming samples of Mathematica?

I am trying to play with some linear programming examples of Mathematica as ExampleData[{"LinearProgramming", "blend"}, "Equations"]. It gives me the MPS format of ...
4
votes
1answer
149 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 ...
5
votes
1answer
269 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
1
vote
1answer
197 views

List comparison in constraints for Minimize

I am trying to solve an optimization problem, a simplified version of which is as follows: ...
4
votes
3answers
417 views

How to find the minimum of this constrained expression?

Let $x$, $y$, $z$ be three nonegative real numbers and $x^2 + y^2 + z^2 = 5.$ Find the minimum of the expression $$E=\dfrac{1}{2}x^2 y^2 + y^2 z^2 + z^2 x^2 + \dfrac{96}{x + y + z + 1}.$$ I tried ...
3
votes
1answer
197 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
2
votes
1answer
250 views

How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? ...
0
votes
1answer
938 views

How to find the global maximum of a function? [closed]

I tried the following but plotting the function clearly reveals that there is a global maximum around $r = 7$ (here $a = 0.53$) ...
1
vote
2answers
604 views

Area of the largest rectangle bounded by $y=x^2$ and the x-axis within the unit interval

I am trying to find the area of the largest rectangle (whose sides are parallel to the coordinate axes) contained in the region bounded by the graphs of $y = 0, y = x^2,$ and $x = 1$ using ...
2
votes
1answer
112 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
2
votes
2answers
268 views

NMinimize problem again

Following up my previous question which got great replies, I am now trying to do ...
9
votes
4answers
2k views

NMinimize usage

I would like to minimize functions including the following. NMinimize[{1 - (1 - 1/n)^x - x/n, n > x, x > 1}, {n, x}] However Mathematica complains about ...
0
votes
1answer
172 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
0
votes
1answer
356 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
6
votes
3answers
1k views

Travelling salesman with start and end points for 30 points

I am doing a route optimisation for delivery vehicles and failing dismally. Please see problem statement below. My current solution uses FindShortestTour, but this does not have defined start and end ...
2
votes
1answer
518 views

Problem using the DifferentialEvolution method of NMinimize [closed]

I have a function of 20 parameters, which 3 of the parameters are my physical parameters, and the others are pull terms to fix the errors. The goal is finding the global minimum of this function, to ...
13
votes
3answers
905 views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
0
votes
1answer
85 views
10
votes
1answer
1k views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
0
votes
0answers
411 views

Mathematica, nested optmization [duplicate]

I want to use the solution of Maximize, defined as a function, in another function. Here's an example: ...
3
votes
2answers
140 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 ...
7
votes
2answers
552 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 ...
1
vote
0answers
127 views

How to express this output in the form $X=A.x$?

This problem arose in my stereo vision project. I have two matrices: $$ A = \left( \begin{array}{ccc} \text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & ...
36
votes
7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
1
vote
1answer
146 views

Seemingly simple optimization problem is slow

I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so: ...
1
vote
1answer
490 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
1
vote
0answers
62 views

Using lists as optimization parameters [duplicate]

Possible Duplicate: Minimizing a function of many coordinates Suppose that the function $F[\vec{x}]$ computes a certain polynomial of the elements of the list $\vec{x}$. How can I use ...
2
votes
0answers
406 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
2
votes
1answer
486 views

Restrictions problem

I tried to program a simple linear optimization model and don't know where my mistake lies. The function should be a sum over "t" and "z" from the product of two constants ("e" and "H") and the ...
2
votes
3answers
2k views

Determining the local extrema of discrete data [duplicate]

Possible Duplicate: Local max/min of Mathematica data sets If I have a continuous function f (for example ...
4
votes
1answer
256 views

Maximizing functions with Which statements

I'd like to be able to find the maximum value that my Capex function (see below) generates. This is a fairly simple function so I could just add it up but I have more complex functions of a similar ...
1
vote
1answer
943 views

How to find local minima of a multivariate function with singularity?

I am working on a logistic regression problem which requires minimizing a cost function J[{theta0, theta1, theta2}, X, y] to find the optimal value for fitting ...
2
votes
1answer
300 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
10
votes
1answer
878 views

How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
15
votes
2answers
642 views

How can I speed up the classic GA for graph coloring?

I'm trying to compute the chromatic number of this graph (which is 28): g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col"; My genetic ...
2
votes
1answer
1k views

FindMaxValue and FindMaximum - how to find GLOBAL maximum and not just LOCAL maximum

I will not be able to provide a simple minimum working example here as this seems to be very specific. I have an interpolating function which I substituted into a PDE and then plot said PDE at a ...
8
votes
2answers
929 views

Implementation of a new Game of Life Rule

I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action. I would like to implement the ...
3
votes
1answer
665 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 ...
1
vote
2answers
183 views

Scalar product of two vectors have the least value

In geometry 3D, let $A(1,2,-3) $ and $B(-1,4,1)$ are two points. In the plane $(P):2x-3y+3z-17=0$, find a point $M$ such that the scalar product of two vectors $AM$ and $BM$ will have the least value. ...
4
votes
1answer
223 views

Optimizing a rank 3 tensor

Assume we have the following elements \begin{equation} F_i{}^j \;and\; S_{ij}{}^k, \end{equation} which represent the components of tensorial objects of ranks 2 and 3 respectively, with Complex ...
3
votes
1answer
440 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 ...
1
vote
3answers
216 views

How to find maximum ConditionalExpression among all solutions

For example I want to find solution with maximum value among solutions (and possibly plot it): ...
2
votes
1answer
518 views

Problems with FindMinimum for Constrained Optimization

I am trying to define a simple optimization problem, arising from the discretization of a simple Optimal Control problem. The problem that results is essentially linear, with bilinearities only ...