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

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6
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0answers
104 views
+50

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 ...
4
votes
1answer
233 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 ...
5
votes
1answer
197 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
0
votes
0answers
37 views

Constrained optimization and contraints expressed in terms of other variables [on hold]

I do have constraints 0 <= x <= 1 && 0 <= y <= 1 && 0 <= z <= 1 which I wish to change to ...
1
vote
0answers
26 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
vote
2answers
188 views

Problems finding intersection points between line and generic function

I'm trying to find Intersection points between a line, which is given by 2 points, and a generic function (I want it to be able to handle polynomial functions, circles/ovals, lines and all ...
1
vote
2answers
70 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: ...
0
votes
0answers
32 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
votes
1answer
55 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
votes
1answer
75 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. ...
0
votes
0answers
31 views

Numerical minimization hangs at some steps

Let me briefly explain what I observe and cannot really explain by myself. I occasionally use NMinimize to find optimal parameter sets and sometimes it happens that ...
1
vote
0answers
174 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 ...
0
votes
0answers
34 views

Calculations using imported .csv files

How do I co calculations after I have imported two files (in my case .csv files). I want to take the average of the columns/ rows and then display them to the user in a new chart. Example A1 of one ...
2
votes
1answer
48 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 (...
6
votes
1answer
321 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
0
votes
0answers
41 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
votes
1answer
97 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
117 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 ...
1
vote
0answers
39 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 ...
6
votes
4answers
168 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
vote
0answers
53 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
vote
1answer
115 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
votes
0answers
61 views

How to solve two point boundary value problem numerically

I'm new to mathematica and I'm interested in solving the following optimal control problem: $$ \min_{\rho_1,\rho2}\int_0^Te^{-\beta t}(Nd(t)+\rho_2y_2(\rho_2k_2-C_2)+\rho_1y_1(\rho_1k_1-C_1))dt $$ ...
0
votes
0answers
96 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 ...
0
votes
0answers
47 views

Finding values of a variable fitting a function and minimizing a list of expressions

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 expressions so that each expression is ...
0
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0answers
75 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
votes
1answer
52 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 ...
1
vote
1answer
63 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
votes
2answers
84 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 ...
13
votes
2answers
1k views

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 ...
1
vote
2answers
79 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
votes
1answer
55 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 ...
0
votes
0answers
46 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
votes
0answers
95 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
votes
2answers
219 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 ...
2
votes
1answer
64 views
0
votes
0answers
42 views

Recursive method for the SR1 correction

I am looking to program a recursive formula for implementing the Symmetric rank-one correction. I am not sure exactly where my program fails. Every value is correct except the value for ...
0
votes
1answer
81 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, ...
2
votes
2answers
105 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
votes
0answers
68 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
vote
1answer
118 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 ...
4
votes
0answers
70 views

How to perform Bayesian optimization with Mathematica?

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
votes
0answers
149 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 ...
1
vote
0answers
47 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
191 views

Finding peaks of data

I want to find peaks in my data. My code in a reduced form so far: ...
14
votes
3answers
2k 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
votes
2answers
541 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 ...
17
votes
0answers
226 views

Can code optimize code?

Are there functions, programs or packages that deal with optimizing mathematica code i.e. re-writing ineffecive or convoluted code. -This question has haunted me since I joined SE. The background for ...
1
vote
3answers
109 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: ...