Questions tagged [mathematical-optimization]

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

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14
votes
1answer
2k views

ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
1
vote
1answer
168 views

Minimum value with two factors

Approximate the minimum value of $2e^{x-2}-6x+xe^{x-2}$. Is my input correct? If not can you please correct it? ...
2
votes
1answer
681 views

Maximize over permutations

I have a set $S=\{s_1,\ldots,s_k\}$ and would like to maximize a fixed expression over permutations of $S$: $\max f(x_1,\ldots,x_k)$ with $x_i\in S$ and $x_i=x_j\Rightarrow i=j$. Is there a ...
3
votes
2answers
1k views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
9
votes
3answers
2k views

Cannot find the maximum value of a function

Consider the following function: $a Sin(x)+b Cos(x)$ I tried to obtain the maximum value of this function using MaxValue[]: ...
1
vote
1answer
168 views

Function optimization errors

I have the following Mathematica code (Mathematica version 9): ...
8
votes
2answers
847 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
2
votes
1answer
561 views

Linear Integer Programming with absolute values in objective function

I'm trying to solve a problem of the form $$ \left|a_{1,0}+a_{1,1} x_1 + a_{1,2}x_2\right| + \left|a_{2,0}+a_{2,1} x_1 + a_{2,2}x_2\right|\to\min, $$ where $a_{i,j}$ are real-valued coefficients and ...
11
votes
4answers
215 views

Constraint syntax compaction

Is there a more compact way to represent these constraints: NMaximize[{a+b+c,a <= 5 && b <= 5 && c <= 5...
6
votes
1answer
2k views

Packing squares into a circle

I am currently trying to solve and understand a problem about packing the maximum of squares into a circle. What I am trying to do, is to calculate the maximum number of variable sized squares (with ...
1
vote
1answer
544 views

A problem on generating convex hull

For example, I typed the following: ...
1
vote
1answer
674 views

NMaximize problem

Could anybody explain to me why the following code fails ? ...
2
votes
1answer
389 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
vote
2answers
925 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 \mathbb{Z}_q^...
10
votes
2answers
4k 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. ...
3
votes
2answers
893 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
votes
1answer
117 views

Random variation inside NMaximize

I am using NMaximize as following code. ...
2
votes
1answer
519 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: ...
12
votes
1answer
3k 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
votes
1answer
131 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 ...
3
votes
1answer
797 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 $t \in \mathbb{R}^3$...
2
votes
2answers
412 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
vote
1answer
182 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 ...
1
vote
0answers
142 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
votes
1answer
649 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
votes
0answers
73 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
vote
0answers
338 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
vote
2answers
479 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 $x_0=...
15
votes
4answers
658 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
votes
0answers
235 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
vote
1answer
241 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. ...
4
votes
1answer
246 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
vote
1answer
2k views

using array elements in minimization

I have switched from mupad to Mathematica, however the syntax is completely different here. I want to ...
11
votes
2answers
1k views

Can I use GoogleMap or other GPS data in creation of the Graphs?

I have following graph. ...
1
vote
0answers
137 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 ...
3
votes
1answer
5k 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}}]; ...
4
votes
2answers
852 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
0answers
471 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
votes
0answers
344 views

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

Bug introduced in 9.0 and fixed in 10.0 FindMinimumCostFlow is introduced in 9.0. I updated my Mathematica recently to 9.0.1 cause the previous version was giving ...
0
votes
0answers
51 views

How can I assign EdgeCost for the graph edges? [duplicate]

Here is my code: ...
7
votes
0answers
2k 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
votes
1answer
755 views

Minimizing a Matrix

...
2
votes
1answer
294 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
246 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 ...
2
votes
1answer
349 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
1k 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
240 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
4
votes
1answer
532 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}} - x_{\mathrm{...
40
votes
5answers
17k 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 ...
3
votes
1answer
814 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? (...