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

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1answer
216 views

NMaximize problem

Could anybody explain to me why the following code fails ? ...
2
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1answer
193 views

NMaximize and Conditional Loop

I have developed the following code that simulates a process that decays over time and then returns to its initial state periodically. When I pass a list of random integers in the interval $(1,0)$ as ...
1
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2answers
306 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
6
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1answer
847 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. ...
2
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2answers
268 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 ...
0
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1answer
95 views

Random variation inside NMaximize

I am using NMaximize as following code. ...
2
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1answer
260 views

Finding a fixed vector which minimizes the pairwise distance between noisy elements in two unordered arrays

Let $A$ and $B$ be two sets of $d$-dimensional coordinates of comparible (though not necessarily equal length). For example, here we can set $d = 3$ and have normalized values like: ...
7
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1answer
897 views

Minimization by Nelder-Mead

Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...
4
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1answer
98 views

Exiting FindMinimum when a condition is met

I want to determine if a function f[x] can take negative values. f is expensive to compute and ...
0
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0answers
91 views

Inconsistent results in fits from NArgMin

EDIT: Just realized I had misspelled "inconsistent." I'm using version 7.0. I'm trying to fit a (noisy) data set to a large-order polynomial. (Just for context: there isn't a model for the ...
3
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1answer
444 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 ...
1
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2answers
159 views

Need an efficient method for finding certain matrices

I am trying to write a function which produces square matrices with certain characteristics. The function should have two inputs: number of the rows, n number of ...
1
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1answer
113 views

Working precision for each variable

How can I define working precision for each variable individually for example: Maximize[x y< 100, {x, y}] where the working precisions for ...
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0answers
141 views

Non linear constrained interger Optimization

I need to maximize the equation below which is subjected to some nonlinear constraints Maximize hsum + isum + jsum + ksum + lsum + msum + nsum + osum ...
1
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0answers
76 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
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1answer
273 views

Maximizing trig functions in Mathematica

Just to give some context, my motivation for this programming question is to understand the derivation of the CSHS inequality and basically entails maximizing the following function: ...
0
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0answers
54 views

NMinimize and FindRoot Issues with System of Equations [duplicate]

I am trying to solve a constrained optimization problem with a system of transcendental equations and am running into issues with NMinimize. I have a system of equations (...
1
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0answers
120 views

Conditional solution for system of linear equations

I have a linear equation system Q.m = t, with m unkown and where Q has dimensions ...
1
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2answers
238 views

Finding normals to a curve through a given point

I want to find x on curve $y(x)$, where curve $y(x)$ is perpendicular to point $(x_0,y_0)$. for this I minimize the distance between points $(x,y(x))$ and $(x_0,y_0)$, here's an example for point ...
9
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3answers
372 views

FindShortestTour for charity (or: How can I optimize meal delivery with FindShortestTour?)

I've been wondering about this for a while - but never got around to asking - until I saw faleichik's incredible answer to Mathematica Minecraft. I did some work at a not-for-profit a little while ...
3
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0answers
139 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 ...
1
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1answer
136 views

Feasibility of Linear Program

I have a set of (real) linear equations/inequalities and I want to know whether they have a solution, and to find at least one. The goal is to do this quickly. ...
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0answers
64 views

Initializing Minimization [duplicate]

I am trying to implement a model predictive control scheme in Mathematica, e.g. I optimize input sequences by predicting future outputs. So every time I call the cost function it will simulate the ...
4
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1answer
184 views

How to solve this simple equation?

I want to minimize a quadratic equation, but Mathematica does not solve it and only rewrites the solution. I wonder if there exist any way I can skip the computation by hand (I can solve it using ...
1
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1answer
259 views

using array elements in minimization

I have switched from mupad to Mathematica, however the syntax is completely different here. I want to ...
7
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2answers
596 views
1
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0answers
118 views

How can I say that all quantities need to be positive (and real)? [duplicate]

Can you say at the beginning of a script in Mathematica that you want all the quantities to be positive (and real)? So that in all calculations, only the real values of these quantities will be ...
1
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1answer
1k views

Using NonlinearModelFit to fit data with errors

Assume we have some data of measurements SeedRandom[9]; data = Table[{i,2*(1 + 5*RandomReal[])*Exp[-0.01*(1 + RandomReal[])*i]}, {i, {0, 100, 200, 400, 700}}]; ...
2
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2answers
242 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). ...
2
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0answers
152 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 ...
2
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0answers
278 views

Why my Mathematica 9.0.1 wont work with some samples of Mathematica in Graph Theory?

I updated my Mathematica recently to 9.0.1 cause the previous version was giving me freaky result especially in FindMinimumCostFlow and ...
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0answers
46 views
4
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0answers
334 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: ...
2
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1answer
297 views
2
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1answer
171 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
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1answer
121 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 ...
1
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1answer
147 views

List comparison in constraints for Minimize

I am trying to solve an optimization problem, a simplified version of which is as follows: ...
4
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3answers
365 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
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1answer
187 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
4
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1answer
254 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}} - ...
16
votes
4answers
3k views

Finding Local Minima / Maxima in Noisy Data

I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
1
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1answer
174 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
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1answer
605 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 $a = 0.53$) ...
2
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1answer
328 views

Inequalities with assumptions and constraints

I'm using Mathematica 8 I've been searching the net without luck for this specific solutions: Suppose I have an inequality f(x;M,m)>0 where I KNOW that M>4m and m>0. How can I let Mathematica know ...
1
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2answers
476 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 ...
5
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0answers
193 views

Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events

The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
8
votes
1answer
241 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
0
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0answers
170 views

FindMaxValue vs FindMaximum

I'm studyng the maximum value of the following function ...
2
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1answer
105 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 ...
0
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1answer
777 views

Minimization problem using FindMinimum. Functional value “is not a real number”? [closed]

This question is a follow-up of another one I asked a few days ago. I followed the instructions given in the answer provided by the user that responded. I modified that answer to solve another ...