# Questions tagged [mathematical-optimization]

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

1,785 questions
Filter by
Sorted by
Tagged with
232 views

78 views

### NMaximize - global maximum fail - How to?

Problem : Let x,y,z be non-negative real number whose sum is 1. Find maximum of 0.2x + 0.2y + x^2*z + y*z^2 What I did first was reducing variable. ...
72 views

### How to solve ODEs using deep learning in Mathematica [closed]

I have a number of ODEs (58) with 16 parameters and 9 variables. I want to solve the ODEs to obtain the analytical relationship between the parameters and variables. It is obviously that the ODEs ...
64 views

### Lanczos method to tridagonalize a matrix

I want to tridagonalize a sparse matrix using the Lanczos algorithm. I am working with a very large sparse matrix and I need some speed. In the following for example ...
177 views

### Issue with ConvexOptimization over Matrices with Mathematica 12.2

With Mathematica 12.2, ConvexOptimization was introduced, which, as its name suggests, can solve arbitrary convex optimization problems over matrices [Language ...
87 views

### Solving a system of equations as part of maximizing a multivariable function

This is my code ...
696 views

### Efficient multidimensional optimization while constraining some coordinates

I have a function f[x] with a high-dimensional vector input and a scalar output. I am looking to minimize this function while constraining some of the components of ...
45 views

### Multiple layered FindMinimum

I have a function SQ[b, zQ, zh] where I can find at which zQ it is a minimum, b=0.1 and <...
44 views

### Finding minimum in a list of lists

Imagine I have the following list {{0, {2,3}}, {-1, {5,3}}, {2, {2,6}}, {5, {5,0}}, {0, {1,1}}, {-2, {10,2}}, {3, {4,2}}}; I want to pick the element in the list ...
101 views

### Finding the smallest bounding simplex [closed]

I would like to find the subset of points from a set of d-dimensional points that defines the smallest bounding simplex around a given point. For example, given a set of 3-dimensional points S1 and ...
126 views

### Equation of motion through the Lagrangian with Lagrange multipliers

I ask for advice, I'm a little confused. I have such a Lagrangian. $L=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-\lambda(2x^2+3y^2-1^2)$ Here $\lambda(2x^2+3y^2-1^2)$ is the constraint on the phase variables. ...
101 views

### NMinimize incorrectly says "The problem is unbounded"

I am solving some quadratic optimization problems in Mathematica 12.2 using NMinimize. Mathematica incorrectly gives the error ...
188 views

### How to minimize a function involving NIntegrate?

I have three datasets as follow: ...
192 views

### Finding the Global Minimum

Consider the function ...
62 views

### Trying to solve a basic Lagrangian optimisation problem

New to Mathematica, trying to solve a simple economics problem but having troubles with using Solve and Eliminate. The question: Now suppose that this agent makes two choices, expressed by x and y ...
53 views

### Minimizing a quadratic form: Failed to converge to the requested accuracy or precision within 100 \ iterations

I'm trying to minimize this type of quadratic form: ...
56 views

### NMaximize computes wrong value

This question is a continuation of NIntegrate with a complicated function over the 4-sphere . Now I define a certain new function called "improvement" via: ...
166 views

### Rectangle packing, fixed sizes

I have rectangles of a given size to fit into a larger rectangle of a fixed size, with a specified gap between the packed rectangles. I would like to write some code that optimises the number of ...
62 views

### Parametric Optimization In Mathematica

I want to solve the following problem: $$\max_q \dfrac{q}{a}\left[ (-\log(1-q))^{-a} - (-\log(q))^{-a} \right]$$ subject to $1\geq q \geq 0$ for each $a\neq 0$. Here is the code I used: ...
104 views

### Dense packing of disks with different radii

Let's consider a disk ($D_{1}$) whose center position is randomly generated, but the radius is fixed at $r_{1}$. A second disk ($D_{2}$) of fixed radius $r_{2}$ (with $r_{2} < r_{1}$) is randomly ...
135 views

...
70 views

### Minimizing functional using FindMinimum

Suppose you are given some functional $S$, (with some 'Lagrangian' $L$) $$S[f]=\int_{t_i}^{t_f}L[f(t),f'(t)]dt$$ and you want to find the function $f$ that minimizes it, subject to some boundary ...
64 views

### Finding convex envelope

I need to find largest $a$ such that $1/(ax+1)\ge g(x)$ for all $x$ in $[0,0.5]$. Both functions are convex, and $f$ is implicitly defined below. What is a good way to approach this in Mathematica? <...
40 views

### NMinimize with elimination returns strange results

I have a parameter vectors pars, par1, and a matrix data1 together with a vector result <...
39 views

### NMinimize extremely slow for simple, non-oscillatory function on an interval

The minimum of $f(x) = -(x+1/2 \sqrt{1-x})$ for $x$ between $0$ and $1$ occurs at $x=15/16$ with $f(15/16)=-17/16$. This is a function that Mathematica evaluates quickly, and I have plotted the ...
75 views

### Fail to inverse the Piecewise function embedded in a NDSolveValue

I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver. I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as <...
48 views

### Finding lower and upper limits of a function of four variables [closed]

Is it possible to tell Mathematica to find the lower and upper limits of the following function ...
74 views

### How to prove the following optimization result from Mathematica?

Currently, I am working on a decision problem in Telecommunication. This problem is reformulated under a form of Optimization problem that is: \begin{gathered} {\text{Minimize}}\,\,\,A \hfill \\ ...
68 views

### Nonlinear Model Fitting to Numerical Data with automatic elimination

I have an experimental data set {f,x,y,z} as {{300., 2., 4., 6.}, {500., 0., 4., 25.}, {6600., 1., 15., 9.}, {100., 5., 0., 2.}, {1100., 10., 8., 1.}, {1300., 7., 8., 18.}, {300., 23., 5., 0.}, {400....
32 views

### some details of Differential Evolution

I use NMinimze Function with method Differential Evolution method, to get the optimal solution I don't give any parameters for this method, I accept the default values that mathematica gives as ...
44 views

### Increment FindMinimum range

I have a function SQ[b,zQ,zh] where I want to find at which zQ it is a minimum. The parameters are ...
77 views

### Constricting variables in NMinimize to binary (0,1) value

I am trying to optimize a large function with 1024 input variables using NMinimize. The caveat is, that the function should only be called with each of the variables as a binary value (0 or 1). The ...