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

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Finding function by constraints

I have the following coefficient finding problem: f[x] := a * Log[b*x + c] + d Constraints: f[0] = 1 f[80] = 0.5 I want to find the coefficients of f that ...
4
votes
1answer
281 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=\max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions ...
1
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0answers
107 views

Method used by NMaximize with a binary linear problem

I'm using Mathematica 7's NMaximize to solve a linear programming problem with thousands of 0/1 integer variables, thousands of linear constraints and a linear target. I suppose I could use ...
1
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2answers
117 views

Maximise a function over one parameter that is continuous, and one that is discrete

I have a function that I would like to maximise with respect to two parameters: one continuous, another which is discrete. A simple example of this might be the following: ...
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0answers
77 views

Optimization over 6 vectors

Suppose I have an expression which depends on 6 unit vectors (3 dimensional). Hence, I need to optimize over 12 parameters (every vector contains 3 parameters, but one we can reduce by considering ...
2
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1answer
152 views

i need a swap mutation code (genetic algorithm) in Mathematica?

I'm working on GA coding to optimize the locators position in fixturing system to minimize the error in precision manufacturing.I need a code for mutation (genetic algorithm) in Mathematica. Here, I ...
0
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1answer
1k views

Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. ...
1
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0answers
278 views

Solve set of non-linear equations with least-squares-fitting - constrain results?

I'm trying to solve a set of functions to determine the material properties from a set of measurement values. (To set up this method I just want to fit my model with some already calculated data). My ...
2
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1answer
77 views

Transforming an Optimization Problem into a multi-vector Optimization Problem

I am sitting on an MultiAgent optimization problem trying to solve for a quadruple of variables {e,l,b,c} In a single agent (...
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0answers
79 views

L1-Norm Minimization

I need the function for the L1-Norm Minimization problem formulated here https://reference.wolfram.com/language/tutorial/ConstrainedOptimizationLinearProgramming.html#261990371 ...
4
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1answer
122 views

Question about FindMaximum

I must advise you that I am an almost total novice in mathematica.. However here is my very simple question.. I know the command FindMaximum[{f},{x}] to find the maximum point and maximum value of a ...
7
votes
1answer
242 views

Finding the least positive integer satisfying a quantified statement

I'm studying the convergence of the sequence of functions $f_n:[0,1]\subset\mathbb{R}\to\mathbb{R}$ defined by $$f_n(x)=n^2x(1-x^2)^n$$ for $n\in\mathbb{N}$. These functions converge pointwise to the ...
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0answers
49 views

reset the value of a variable [closed]

Folks, I have a problem in populating a matrix without overriding the values. After performing computations for various values for j, I want to store these values in following matrix. Here is the code:...
6
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4answers
215 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 ...
1
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0answers
111 views

Finding the global extrema of a surface? [closed]

I am trying to figure out how to find the global extrema of the function surface shown below and can't seem to get answers that make any sense. I am using the FindMinimum and FindMaximum functions ...
1
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1answer
234 views

Fibonacci Line Search Method

I am attempting to write a code to find to bracket the minimum of a function using the Fibonacci Line Search Method, I believe my code is well written but I am not ...
0
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0answers
137 views

How to optimize a cost function which involve the solution of a ODE system using the NMinmize?

I have created a cost function, the value of which depends on the solution of a ODE (ordinary differential equation). The parameters of the ODE are not determined, and my goal is to determine them ...
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0answers
101 views

Fun/Frustration With Coding Coding Theory

I have code following from this post: http://math.stackexchange.com/questions/1317722/fun-frustration-with-coding-coding-theory I think I am done with the code, but now I face a single problem. The ...
-1
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1answer
84 views

Find a minimum value which satisfies an equation

I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0 ...
2
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1answer
87 views

Problem in minimizing expression

I am trying to implement bootstrapping (https://en.wikipedia.org/wiki/Bootstrapping_(finance)) of CDS curve. To implement it I am trying to minimize a series of expression. The minimum value of ...
2
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2answers
118 views

Finding Minimium Periapse Distance Between Spacecraft and Planet

I have the following simple model that simulates a spacecraft orbiting Mars. What I'm hoping to do is be able to find the periapse radius of the spacecraft as I did below, except instead of using ...
1
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2answers
177 views

FindMinimum and WhenEvent

Is there any way to incorporate WhenEvent[] into the FindMinimumfunction ? I'm currently trying to minimize an interpolating function with FindMinimum (since the origional function is to cumbersome ...
2
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1answer
226 views

NMaximize with Nelder-Mead method fails to convergence when tolerance set too high

Recently I have been working on a optimization problem for which I use NMaximize with Nelder-Mead method. In general, I have to check a lot of systems which are built automatically. I want to skip ...
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0answers
54 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
5
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0answers
176 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
9
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2answers
301 views

Relaxation of Mass-Spring System with Pinned Masses

Problem Assume that four masses are connected to each other by springs while two of them are pinned down at their initial positions. Find the position of masses when system is at its minimum (...
0
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1answer
125 views

Both FindMinimum and NMinimize have trouble

I'm trying to minimize a function I wrote, in a not entirely elegant (but functional) way. As a side note, if you have advice on how to write this in a smarter way, that's also welcome. In any case, ...
4
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2answers
204 views

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 ...
3
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0answers
88 views

Symbolically Minimizing a Max function

I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ...
1
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1answer
126 views

Equation solution using minimization

I have an equation F[x,y]=0. I need to plot y as a function of x. Due to the properties of ...
5
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0answers
94 views

How to perform Bayesian optimization with Mathematica? [duplicate]

Does Mathematica have any Bayesian optimization methods for learning hyper-parameters? Practical Bayesian Optimization of Machine Learning Algorithms Jasper Snoek, Hugo Larochelle and Ryan P. ...
0
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0answers
258 views

Optimization method L-BFGS-B

I am comparing a result of optimization using R and Mathematica. Mathematica (NMaximize) has found a significantly better (global optimum) result then R (using L-...
1
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0answers
115 views

How can I calculate Lagrange multiplier and the critical points with Mathematica? [closed]

I have constraints and a function I want to know the critic points but is there a way that I can compute this method so that I can see results faster
3
votes
1answer
977 views

Finding peaks of data

I want to find peaks in my data. My code in a reduced form so far: ...
18
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3answers
4k views

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 ...
8
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2answers
666 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
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3answers
258 views

Minimize method is not giving minimum. Why?

I was doing an optimization but facing a problem getting what exactly Minimize function do. I run the following code: ...
16
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2answers
588 views

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, <...
3
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3answers
127 views

Minimizing Multiple Functions

I'm trying to write a script that will minimize a given set of functions. The homework problem I've been given lists a set of dietary information, and I'm supposed to build the optimal salad based on ...
0
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0answers
69 views

Which method to use for finding maximum without actually computing optimization function explicitly?

I am new to Mathematica and I am currently working on an optimization problem. The optimization function that I have easy to calculate for some assignment of variable but it is very difficult to ...
2
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1answer
345 views

How to build a list of constraints for NMinimize

Let's say I have aset = {-1, 0, 2}. I would like to create a variable Var that takes values from that set, i.e. ...
4
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1answer
143 views

What is the status of the FindMinimum method “QuadraticProgramming”?

As a method option to FindMinimum "QuadraticProgramming" is still a valid option. It has the advantage of being significantly ...
0
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0answers
108 views

Constrained optimization and problem with complex numbers

I am trying to solve a constrained optimization problem with an implicitly defined function $\pi$. The problem is non linear and of high order, so I use numerical methods instead. The code I use is: <...
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0answers
130 views

Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
2
votes
1answer
131 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
6
votes
1answer
545 views

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. ...
1
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2answers
278 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 ...
3
votes
1answer
107 views

How can I change a lot of parameters to Real? [closed]

Because of some formulas with Conjugate in a notebook, I have to tell mathematica to change a lot of parameters to Real! I know that I can use Refine with Element or Assumptions: ...