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

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2
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1answer
75 views

Plot a function after taking the supremum with respect to one variable

Assume given a continuous function $f$ with 2 variables, say $x$ and $y$. $x$ takes values on the interval $I$ and $y$ takes values on the interval $J$. I would like to know how to plot the function $...
0
votes
0answers
34 views
0
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0answers
54 views

Minimization with constraint define over a region

I would like to perform a 2D electrostatic minimization between two charged ellipsoids, provided that they should not penetrate each other; they can touch but they are hard ellipsoids. Here is what I ...
2
votes
1answer
60 views

Principal Axis Maximization

I know that, in order to use PrincipalAxis, for example in FindMaximum function: ...
2
votes
1answer
52 views

Trouble with some optimization

I am attempting to use Mathematica to solve an optimization problem related to mechanism design (4-bar). The optimization problem is basically the following: 1) Solve these two simultaneous loop ...
1
vote
1answer
77 views

Maximisation problem not working

I am trying to solve the following optimisation problem, but Mathematica is not providing me with a solution: $$\max_{x_{1},x_{2},e_{1},e_{2}}\theta_{1}\ln(x_{1})-e_{1} + \theta_{2}\ln(x_{2})-e_{2} \\...
1
vote
0answers
62 views

NMinimize / adding constraints

I have a quick question: in question:Solving an ODE with boundary conditions at infinity and 0//different problems, I asked for help concerning a differential equation- however, the whole solving ...
0
votes
1answer
148 views

Solving linear system with constraints

I need to come up with a solution for a rather, odd situation. Let's say I have an $M \times N$ matrix called ${\bf A}$, and I would like to solve it for ${\bf x}$ where $b_1 \le {\bf A} {\bf x} \le ...
2
votes
1answer
54 views

Does 'True' stand for 'Else' in Maximise function output?

Maximize[a x^2 + b x + c, x] gives this solution: Does the word 'True' stand for 'Else' here?
9
votes
0answers
97 views

LinearProgramming returns an invalid null solution that apparently doesn't satisfy constraints without any warning

Bug introduced in 10.3.1 or earlier and persisting through 10.4.1 While searching to answer the question Solving the magic backyard puzzle with MMA at some time I composed a set of arguments ...
3
votes
2answers
154 views

Can't find maximum of a function on a region

for h=0.2 I'm trying to find the maximum value of (-h^2/3)*(-1/x^2) subject to ...
1
vote
2answers
127 views

How to visualise (graphically) this optimization problem in Mathematica?

I have an optimization problem in the form max $(a-\bar{a})(b-\bar{b})$ subject to $a+b=1$ Here $\bar{a}$ and $\bar{b}$ are known values and both of them are >0. The solution is given by $a=(1+\...
9
votes
1answer
789 views

Max & min distance between two moving points

I am trying to find the minimal and maximum distance between two moving points with Mathematica in an interval. For example, ...
0
votes
0answers
68 views

Kernel crashes during `LinearProgramming`. Can you reproduce it?

Using the code from this answer for a sufficiently large problem setting crashes my kernel. I'll copy/paste the code here: ...
1
vote
1answer
64 views

Efficient maximisation of log-likelihood

I would like to efficiently find the maximum $(\sigma,\lambda)$ for the log-likelihood of the derived distribution below. I only need $\sigma$ and $\lambda$ to one decimal place - so not very precise. ...
0
votes
0answers
23 views

Casting an optimization problem into least-squares form for Levenberg-Marquardt [duplicate]

I would like to use the function FindMinimum[] with the Method LevenbergMarquardt to this function: ...
2
votes
1answer
216 views

Error with FindMinimum. The Message is FindMinimum::cnpcons

I want to run a rather demanding check of feasibility. I have 3565 non-negativity constraints for my variables, and one that makes them sum to a certain budget they shall not surpass. I also have ...
1
vote
1answer
230 views

Using the Levenberg - Marquardt algorithm to minimize a user-defined function

I wrote a function in Matlab that optimizes another user defined function using lsqnonlin with 'levenberg-marquardt' option. Now, I'd like to use the first to ...
1
vote
1answer
117 views

Invalid computation of maxima

I am finding the following minimum FindMinimum[{ Abs[ ArgMax[f[q, n, b, b0, b1, t, s], b] - b1 ] }, {b1, -0.5}] given ...
7
votes
1answer
218 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 ...
2
votes
1answer
48 views

How to couple NIntegrate with FindMinValue

I have a problem with a correct transfer of values of parameters when NIntegrate (and some subsequent functions) are coupled with minimizing procedures in ...
1
vote
1answer
124 views

How to Minimize an NIntegral

My problem is to minimize in Mathematica a numerical integral. The command FindMinimum[With[{R=2.5},NIntegrate[(R*r1*a)*Sin[r1*a],{r1,1,R}]],a] does calculate ...
1
vote
0answers
84 views

Possible memory leak in FindMinimum? (MMA v10.0)

So I was running some code when I noticed Mathematica was gulping memory, and after some debugging I think the culprit is found. It turned out the function ...
1
vote
1answer
76 views

How do I write a function inside a ArgMin

I want to solve this ArgMin[NIntegrate[(Tanh[x] - Erf[x/a])^2, {x, -5, 5}], a] and it does not work, what is the correct way to do this? ...
1
vote
1answer
68 views

Finding a vector many times

I have a vector matrix of profits say prof= {{1, 1, 1, 1, 1}, {2, 2, 2, 2, 2}, {3, 3, 3, 3, 3}, {4, 4, 4, 4, 4}, {5, 5, 5, 5, 5}}; I have a "terminal value ...
6
votes
0answers
106 views

Customized StepSize control in unconstrained gradient-descent optimization

I have a type of minimization problem I frequently solve that involves warping a large 2D triangle-mesh (~25,000 vertices) to fit a model. In the mesh, vertices carry the empirical measurements (each ...
3
votes
0answers
101 views

Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
4
votes
1answer
172 views

Goal optimization: finding the best combination of capacitors and resistors resulting in given properties

I want to edit @MarcoB answers (because the code he gave doesn't answer the question appropriately)->(the function that need to be optimised is not implemented as asked) But it seems like I am having ...
1
vote
1answer
122 views

Optimizing best fit circle to given data set [duplicate]

Given a set of data, I have plotted a slowness curve for a p-wave resulting from the given data. A slowness curve is just the reciprocal of the velocity of the p-wave. What I need to do is find a ...
0
votes
1answer
58 views

Basic question about loops in mathematica

I am very new to Mathematica programming and am trying to find the optimum of a numerical integral for various values of a parameter. Here is the basic code for one parameter value that runs fine - I ...
24
votes
3answers
839 views

Exponential fitting - isn't actually a BUG there?

There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds ...
2
votes
1answer
129 views

How to transform the output of Minimize/Maximize into a function

I want to create a function directly from the output of Maximize. Specifically, I have the following function $f(l,h,d,a)$ that I want to maximize with respect to $...
1
vote
1answer
76 views

Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
4
votes
0answers
111 views

How is the multi-class support vector machine classifier implemented? [closed]

I am using support vector machine (SVM) method with Classify to do multi-class. Can anyone tell me the reference (paper) used by Wolfram Mathematica to develop the ...
1
vote
1answer
68 views

Running this expression in Minimize function

So I got this expression here (written in pure text): ...
2
votes
1answer
205 views

Maximized value of a function as an additional constraint on a variable

I want to maximize a function $f(b, h)$ with respect to its arguments and subject to some additional constraints. If these constraints are satisfied, $f$ is increasing in $h$. I then want to find an ...
1
vote
1answer
82 views

How to find a maximum value in a rotated parametric plot?

Let me just give you a bunch of tables to reproduce the problem. Here they are ...
5
votes
2answers
356 views

Finding minimum and maximum of implicit functions

The equations of the system are ...
6
votes
1answer
108 views

Simulated Annealing, SearchPoints and InitialPoints options set at the same time

I have a function that needs to be minimized. Since the function depends on real-time data (which is fetched every few hours, and the function is redefined according to the new data), I have to run ...
4
votes
0answers
64 views

NMinValue , NMaxValue , NMinimize and NMaximize behave poorly for 2-dimensional function unless the constraint is posed as an ImplicitRegion

I am making a plotting function where I need to know the max value the function takes over the given 2D range. I noticed a difference between the behavior of ...
3
votes
0answers
90 views

Is there an analogue of Evaluated->False (in FindRoot) for FindMinimum?

I guess functions like FindRoot, FindMinimum, etc puts the estimation number into the expression, and then do other calculations....
0
votes
2answers
97 views

How to get the correct answer of this expression with Minimize? [closed]

I want to find minimum value of the expression $$P = 13 x^2 + 12 y^2 + 22 z^2$$ such that $x y + y z + z x = 1$. I tried ...
4
votes
1answer
152 views

FindMaximum “is not a real number at” nrnum problem

I'm experiencing a problem using FindMaximum that I don't understand (due to my newbie knowledge of Mathematica's syntax). That is, FindMaximum sometimes returns a (correct) answer, but sometimes ...
2
votes
1answer
72 views

How can I minimize a function with respect to the number of its variables?

Given some $d \in \Bbb{Z}_{>0}$, $t \in [0,1]$, and $0 < a < b < 1$, fix $I = [a,b]$. I'm trying to compute $$ \min_n \min_{E_n(t)} f_d(\mathbf{x}) $$ where $n \in \Bbb{Z}_{>0}$, $$ f_d(...
10
votes
1answer
403 views

Shortest tour with vertex priority

I changed the title of my question and tried to simplify formulation of the problem. I solve a very big vehicle routing problem. I divided this one big problem on many small sub-problems. Each small ...
1
vote
1answer
53 views

How can I improve the result of this non-linear optimization?

Given a positive integer $d$ and some $0 < t < 1$ I would like to find a global minimum1 for $$ \sum_{k = 1}^n d^2 \tan\left(\frac{\pi}{2} \, x_k\right) + 8 d $$ over $n \in \Bbb{Z}_{> 0}$ ...
5
votes
2answers
99 views

How to find alignments of interlocking shapes?

I'm searching for the ways to align interlocking shapes, that is, finding the locations and rotations that maximize the arc length at which they touch. For simplicity, I'm assuming 'shapes' are one ...
1
vote
1answer
54 views

How to solve Quadratic Program in vector form?

I've gotten Q matrix and Y vector, Q matrix is a 7x7 matrix, but the "NMinimize" in wolfram seem can only solve the real number not vector, how to solve it in vector form? (alpha 7x1 vector, Y 7x1 ...