# Questions tagged [mathematical-optimization]

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

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### How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
479 views

### What is going on in this plot?

Plot[{ArgMax[Cos[t] Sinc[2*Pi kl (Sin[t] - 1/Sqrt)], t]*180/Pi, 45}, {kl, 0, 10}, PlotRange -> Full] I want to know what causes this, and how to fix it ...
417 views

### ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
228 views

### Is there any way to speed up this code that's Maximizing a function got from numerical integration?

I have this code below, which is calculating the Binding energy of an electron in a Quantum Well Wire with a hydrogenic impurity in it. Well you don't have to care much about what kind of calculation ...
156 views

### Minimizing NExpectation for a custom distribution

As discussed and advised in Meta: Migrate a question..., I've copied a 2012 posted question from StackOverflow (posted before this site began running), which has gotten a lot of attention (but after 3 ...
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### A puzzling maximization issue using Abs[ ] in the constraints

Consider the following pair of commands. Maximize[{x^2 + y^2, Abs[x] <= 1, Abs[y] <= 1}, {x, y}] $\{2, \{x \rightarrow -1, y \rightarrow -1\}\}$ ...
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### FindMaximum failing on a trivial problem [closed]

I am trying to solve a trivial optimization problem with FindMaximum but for some reason it is not going. I reduced the problem down to the following non-working ...
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### NMinimize with NIntegrate (crash in symbolic evaluation, memory leak)

This is a "common" problem from what I've seen, but with a different spin. I have a function I use often that finds a fit of an expression to another expression with some free parameters (e.g. for ...
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### Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations

The formal problem The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
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### StableMarriage vs. FindIndependendEdgeSet: How to use the procedure FindIndependendEdgeSet as a Gale-Shapley algorithm?

From Help, the procedure StableMarriage was an element of the Combinatorica, but it is available in the built-in ...
166 views

### FindShortestTour causes kernel crash

I have contacted support, CASE:4075709 UPDATE I have received reply from wolfram support. They have confirmed that this is indeed a bug. There are lots of sets of data that can cause the Kernel to ...
371 views

### How to determine reason for kernel crash? -> Nelder Mead optimisation

I am making use of the Nelder Mead algorithm inside Mathematica's NMaximize to find a parameter set by solving the Schrodinger equation for a given system. (see ...
594 views

### FindMaximum of Interpolated data set

Probably a fairly easy one; but I'm drawing a blank I would like to find the maximum of an interpolated data set. I've tried using ...
402 views

### Finding a center and radius that minimizes total distance

I have a list of $d$-dimensional data points $x_i$, and I want to find a $d$-ball which minimizes the sum of the squares of distances between the surface of the ball and the points. In other words, I’...
339 views

### What is the best way to track the gradient to a local minimum?

Given a function of multiple variables, and some initial conditions, I would like an efficient way to track the gradient to the local minimum of that function. Two options spring to mind — to either ...
580 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 ...
217 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 ...
769 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 ...
566 views

### FindMinimum: How can I know which method Mathematica has used?

I have been using FindMinimum to find a local minimum of a non-linear function within a constrained region. How can I know which method Mathematica has selected to find the local minimum? Thanks in ...
1k views

### Packages for Semidefinite programming

This question has already been asked here. I am not sure, whether I should have asked this question as a comment of an old question or in the general programming forum of stackexchange. Moderators ...
335 views

### Risk-return trade-off — solving a convex optimzation

I try to convert a convex optimisation (cvxopt) example to the Wolfram Language from python. Source of the python code: Risk-return trade-off Please advise me on how to convert the following python ...
956 views

### Graphically solving a linear programming problem

I try to realize the graphical linear programming method. Here is my code ...
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### Using compiled function inside NMinimize

Consider this code: ...
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### Visualization of iteration procedure in NMinimize

I have this optimization code: ...
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### How to generate optimal solution and order the rest

This is a decimal maze, you start with 100 points and you must choose the path that gives you the highest score. Rule: You should not go twice for the same point and the same segment. My question: Is ...
191 views

### Test existence of a path from one side of a graph to another

I'm trying to determine how I can test if a path exists from one side of a graph to another as efficiently as possible. If I have the Lines given by: ...
440 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 ...
318 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: ...
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### Solve Lagrange multipliers optimization problem

I have two nested solid figure, where $V(a,h,\tau)$ defines the volume and $A(a,h,t)$ defines the surface. The outer solid figure is parametrized in $a_s$,$h_s$ and $t_s$ (they share a common center). ...
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### Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
222 views

### NMinimize Example from Wolfram Documentation Center

Here is the third example of NMinimize function from Wolfram Documentation Center at Possible Issues section. ...
826 views

### Visualizing the Lagrange Multiplier Solution

This question is based on work in Susan Colley's Vector Calculus, 4th ed. The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint $g(x,y,z)=3x+y+2z=13$...
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### 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: ...
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### MaxDetect speed

What's the fastest way to find the local maxima of a 2D list? E.g. ...
302 views

### Minimizing a function with a constant $l > 0$

I'm VERY new to Mathematica and would like some help with minimizing a function. $$f(x) = \frac{1}{2} \sqrt{\frac{\left(l^4+x^4\right)^2}{l^4 x^2}}$$ I want to find which $x-value$ (probably ...
460 views

### How to make the computation of a minimum efficient?

I have a $80\times 80$ matrix $A$ and a vector $P$ and I want to compute efficiently the following minimum $$\min\{n\in \Bbb N :\|A^nP\|_\infty < 1\}$$ Then I defined my matrix and vector in ...
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### Reordering numerically calculated eigenvalues assuming smooth dependence on a parameter

As was discussed in a different question here on SE (link) if you compute eigenvalues numerically of a matrix which depends on a parameter y, the resulting plot of ...
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### 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 ...
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### 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 ...
154 views

### Assign Error bars for y-intercept

I have some data (x,y) with error bars in y direction: ...
925 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 ...
3k 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 ...
491 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 ...
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### Which algorithm does Mathematica use for “RandomSearch”?

Recently I have used Mathematica for minimization of certain functions and I have realized that even though it lasts much longer, the method "RandomSearch" functions much better than the other methods ...
517 views

### Defining a non-linear optimization-problem

Consider the following non-linear optimisation problem: ...
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### Strange results when finding a maximum subject to constraints?

I'm using 11.1.1, and I tried running the following: ...
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### Different results for MaximumLikelihood depending on method?

When I used this command: ...