Questions tagged [mathematical-optimization]

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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2answers
175 views

Formulating a tailor-made Maximum Flow problem in a directed graph

Let a digraph, G, be given, where t[i,j] and a[j,i], respectively, denote transfer capacity ...
4
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2answers
1k views

Finding minimal distance between two surfaces

This code will display two parametric surfaces: ...
10
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4answers
904 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? ...
8
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4answers
1k views

Finding the point of minimum distance between two parametric functions

I have two functions re and rm, for which I computed the minimum distance between them. Now I would like to add a point at the ...
8
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1answer
644 views

NMinimize go out of bounds on some linear constraints

I'm trying to minimize a non-linear function of four variables with some linear constraints. NMinimize on Mathematica 8 seems to go out of bounds on some constraints giving complex values of the ...
6
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2answers
476 views

Techniques to find all local minima of black box function with n continuous derivatives?

I have a blackbox function f on [a,b] that is known to be continuous, and has n continuous derivatives. The function uses polynomial interpolations (but isn't a polynomial interpolation itself), so no ...
5
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2answers
513 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.: ...
5
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4answers
537 views

Minimax optimization in Mathematica

Mathematica has functions for constrained nonlinear maximization or minimization of functions, via FindMinimum and FindMaximum ...
4
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0answers
276 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 ...
2
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2answers
603 views

Fitting a variable using multiple equations

I would like to find the best fit of two variables for a number of approximate equations, such as: 1x+2y+2=7.04 2x+y+4=7.98 1.5x+1.5y-2=2.53 1.8x+3y-1=6.77 That ...
1
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1answer
193 views

Printing from the function to be minimized in FindMinimum

I know that there is an option EvaluationMonitor for various numerical computation and plotting functions. But I am curious, why a simple ...
1
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1answer
94 views

3D-Plot optimization results for varying parameter values

Before starting, FYI: This is a question related to 3D Plot the result of local Minimize with varying parameter values Consider my objective function, $objF$: ...
6
votes
2answers
247 views

Counterpart of Maple's LSSolve in Mathematica

I am a great fan of Mathematica. Unfortunately, due to some specific tasks I had to move to Maple. I think it's my lack of info that is not letting me do those tasks. That is why I am asking some ...
5
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1answer
611 views

Why does NMaximize does not follow the constraints that were given to it?

(someone may want to mark it as a duplicate, but I still have to ask! I just can't figure out why!) ...
5
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1answer
596 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
5
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2answers
1k views

Can't find maximum of a function on a region

for h=0.2 I'm trying to find the maximum value of (-h^2/3)*(-1/x^2) subject to ...
4
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1answer
280 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 ...
3
votes
1answer
180 views

Simplifying Expressions for FindMinimum

I am currently trying to apply the FindMinimum function to find the lowest energy of an expression. My current expression as of now is relatively complicated. It is the summation of 48 similar terms, ...
2
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3answers
219 views

Optimization of ODE with respect to the initial condition

One has a (system) of ODEs with a one-parameter family of initial conditions. For example, ...
2
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1answer
706 views

How to enforce constraints in NMinimize

I am trying to minimize a function EtotalEM[R,Δ] that is defined only for Δ <= R/ ArcSinh[1] (approximately: ...
1
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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? ...
1
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1answer
112 views

Efficient maximisation of log-likelihood

I would like to efficiently find the maximum $(\sigma,\lambda)$ for the log-likelihood of the derived distribution below. I only need $\sigma$ and $\lambda$ to one decimal place - so not very precise. ...
0
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0answers
70 views

3D-plot of a maximization of a definite integral

I'm applying the answer (If method) suggested by 'ThatGravityGuy' in this post in a more complicated case. Consider my objective function (pardon its formidable ...
0
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1answer
1k views

NMinimize to optimize function Module

I am using Nminimize for simulation based optimization. I define the objective function (simulation with a variable "a") as a module to be used in the minimization. ...
26
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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 ...
13
votes
4answers
390 views

Optimization of function taking a permutation

I have a function $f$ which takes a permutation $P$ of the integers 1-100 in order to give a numerical value $f(x)$. The function is given by a black box, but is relatively "smooth", so should be ...
12
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2answers
371 views

Time constrained optimization?

I'm trying to solve a maximization problem that apparently is too complicated (it's a convex function) and NMaximize just runs endlessly. I'd like to have an approximate result, though. How can I ...
10
votes
1answer
1k views

Max & min distance between two moving points

I am trying to find the minimal and maximum distance between two moving points with Mathematica in an interval. For example, ...
26
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1answer
390 views

FindMinimum doesn't increase step size when necessary

(Cross-posted on Wolfram Community.) I've spent much time finding a minimal example demonstrating this problem with FindMinimum. Normally one faces this problem ...
11
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3answers
512 views

Minimum energy path of a potential energy surface

I have calculated the energies of a molecule by varying two parameters (Data points are here data). I want to find the minimum energy path from the point (180.0, 179.99, 21.132) to (124.5, 124.49, 0) ...
15
votes
4answers
645 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 ...
6
votes
3answers
909 views

How to use a compiled function in numerical optimization

I'm trying to wrap my head around function Compile. So, this is a spin-off question from: a previous question on using compile[] correctly. I have a function that ...
16
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1answer
493 views

Bug in plotting function using FindMinimum?

Bug introduced in 10.0 and persisting through 11.0.1 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of ...
7
votes
1answer
425 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 ...
6
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0answers
384 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
4
votes
1answer
277 views

Solving optimal control problem when input is constrained

Given a linear time-invariant system: $$x'(t)=Ax(t)+Bu(t)$$ with initial state $x(0)=x0$ and final state $x(T)=xT$. The performance measure to be minimized is: $$∫_0^Tu(t)^2dt$$ The most important ...
3
votes
2answers
555 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 ...
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. ...
8
votes
3answers
435 views

Numerical minimum of a one-valued function

Bug introduced in 12.0 [CASE:4332003] My problem is that the Kernel cannot finish computation and eats up memory when a simple constraint like 0 <= x <= 2 is ...
7
votes
3answers
761 views

Not able to get a solution to a Lagrange Multiplier Equation

I assigned several constrained optimization problems to my calc IV students to solve with Mathematica, but this one is being stubborn. The function to optimize is: f(x,y,z) = y Exp[x-z] with the ...
6
votes
2answers
291 views

Using least independent rectangle area to separate every point

Description I want to add vertical line and horizonal lines between data to make every point have an independent rectangle area. In addtion, every independent rectangle has a number $1,2,3,4,5,\ldots$...
5
votes
1answer
3k views

Finding peaks of data

I want to find peaks in my data. My code in a reduced form so far: ...
5
votes
2answers
249 views

Parallel function evaluation for minimal value

I am asking myself, if the evaluation of a function f looking for a minimal value over a discrete set of values can be parallelize (brute scan for a potential ...
5
votes
3answers
1k views

FindMinimum works only if you know the answer

I am processing SNe Ia data and using FindMinimum to try and extract two values: t1 and a0. The FindMinimum value works only if I supply values that are close to the answer. If I provide no starting ...
3
votes
1answer
356 views

How to define and plot a maximum function?

Define a function $g$ as follows: ...
1
vote
1answer
185 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/...
11
votes
1answer
354 views

Experimental`NumericalFunction in NMinimize solution

I try to make a number of optimizations using this code: ...
7
votes
1answer
576 views

Is there any strategy to have a compiled version of FindFit or NonlinearModelFit?

Disclaimer: This is not a precise question with a definite answer. I know that neither FindFit nor NonlinearModelFit is in the ...
6
votes
0answers
81 views

Caveats of LinearProgramming on Integers domain

When using LinearProgramming with the Integers domain, Mathematica issues the following warning: ...
6
votes
1answer
208 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...