# 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 all the local minima/maxima in a range

I want to find : all local maxima in range all local minima in range From those points I can interpolate and combine functions upper and lower boundary. What I am really interested in, is the mean ...
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### Shaving the last 50 ms off NMinimize

The epilogue: A paper where the below answer is used was published. The answer below is cited among the references:) The background: I have to fit an objective function for ~10 000 datasets in near ...
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### How to work with Experimental`NumericalFunction?

This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?" Oleksandr R. correctly states in the comment: A ...
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### How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
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### Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
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### 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 ...
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### Identifying critical points/lines of 2/3D image/cubes

Upshot I am interested in identifying critical points of a 3D field/cubes (maxima, minima, tube-like and wall-like saddle points) and 2D field/image (maxima, minima, saddle points). I.e. the ...
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### 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 ...
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### how to get $n$ equidistributed points on the unit sphere

We can get $n$ equidistributed points in the unit circle using CirclePoints. But how do you get $n$ equidistributed points on the unit sphere(surface of a ball)? ...
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### Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, <...
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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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### Find maximum value of interpolation function - obviously wrong result

Minimizing and maximizing interpolation function has already been asked and answered, see here for example. Yet, I observe a strange behaviour. Well, I can understand that the wrong guess of ...
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### Finding all maxima and minima of a function

To find all (global and local) extrema of a function in $\mathbb R^3$, I have written the following. Example function: ...
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### Differentiating functions of vectors/matrices?

I'm dealing with derivatives of scalar functions of matrices and wondering if Mathematica can help me here. The standard approach of expanding it in terms of components is cumbersome. As an ...
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### $L_\infty$ norm minimization

I write supplemental explanation to render my aim of optimization. First Consider discrete time linear system below: $$G(z)=\frac{1-e^{-0.3T}}{z^{100}(z-e^{-0.3T})}$$ ...
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### 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, ...
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### How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
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### Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
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### Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
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### Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
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### Minimizing a function of many coordinates

I'm trying to obtain a series of points on the unit sphere with a somewhat homogeneous distribution, by minimizing a function depending on distances (I took $\exp(-d)$). My points are represented by ...
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### How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
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### Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
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### How to find local minima of data using PeakDetect

One of the great new function in v10 is PeakDetect. It can detect peaks (local maxima) according to desired sharpness as shown in this example: ...
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### What alternative notation of subscripts/superscripts that are also treated as SYMBOLS in Mathematica?

I tried to avoid using the subscript $A_0$ in the Module, and get an error with $A[0]$. ...
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### optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
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### Optimization of a portfolio of stocks

I would like to use Mathematica to perform an optimization of a portfolio composed by 10 stocks. I did the first part to compute yields and expected yields, but I don't know how to finish the ...
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### Expressing a polynomial as a sum of squares

I encountered a degree 4 polynomial in 8 variables f(a1,a2,a3,a4,b1,b2,b3,b4) that I suspect can be written as a sum of squares. While sostools in MATLAB would find ...
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### 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 ...
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### Which methods are available for NMinimize?

I can't find in the documentation the list of methods available to NMinimize[]. Is there a way to get this? The NMinimize page in Documentation Center mentions only ...
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### Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
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### 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 ...
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### Minimax optimization in Mathematica

Mathematica has functions for constrained nonlinear maximization or minimization of functions, via FindMinimum and FindMaximum ...
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### 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!) ...
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### 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: ...
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### FindMinimum, NMinimize, etc. with external process [duplicate]

I was hoping to be able to use MMA's minimization power to work with an external process. I want to minimize the function 'TryThisNumber[x_]' which sends the value of x to something external and gets ...
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### adding a point in a manipulate command

I am having trouble adding a point to mark the Min values of each parabola when using the Manipulate command? ...
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### How to compute higher iterations in mathemtica

I have the equation $u^{\prime\prime}(t)+u^{2}(t)-t^{4}-2=0$ such that $0\leq t\leq 1$and also I have $u(0)=0$ as well as $u(1)=1$. Noe the exact solution of the equation is $u(t)=t^{2}$. Now I ...
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### 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 ...
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### 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 ...
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### Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
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### Can I use GoogleMap or other GPS data in creation of the Graphs?

I have following graph. ...
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### Simulated Annealing Convergence

I am using Simulated Annealing method for a simulation based optimization of a process that has 3 variables, using NMinimize. I print the input/output during every ...
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### Given square matrices A and B, how to solve T obeys Transpose[T]. A . T = B? [duplicate]

Dear Mathematica experts, Given two square matrices, A and B, how do we use Mathematica to solve a matrix T such that T satisfies this matrix equation? (Here we have A,B,T $\in$ general linear matrix ...
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