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

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2answers
129 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
13
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9answers
2k views

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 ...
0
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0answers
110 views

Problems with NMinimize

I have written some functions that take a matrix and find its minimum inner product with a specific set of vectors ...
3
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0answers
70 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 ...
4
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0answers
57 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 ...
0
votes
2answers
90 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 ...
3
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1answer
120 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 ...
1
vote
1answer
277 views

How to minimize the sum of squares of deviations from the mean?

I am trying to minimize the sum of squares of a deviation from the mean applying the following: Minimize[Sum[(Subscript[x, i] - μ)^2, {i, 0, n}], x] It returns ...
1
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1answer
71 views

Variables input generation for Minimization in High dimensional space [duplicate]

I'm currently doing optimization in a high dimensional space. I was thinking of giving FindMinimum (or NMinimize not certain ...
2
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2answers
163 views

Maximizing over an integral with a single parameter

There is probably a neat approach to solve this problem...but can't get to it at the moment. How do you maximize an integral with respect to a single parameter? My code below produces error messages. ...
10
votes
1answer
396 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 ...
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
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1answer
51 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 $n \in \Bbb{Z}_{> 0}$ ...
1
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1answer
43 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 ...
10
votes
1answer
186 views

DifferentialEvolution scaling factor randomization

Using NMinimize for finding global minima, one can choose the DifferentialEvolution method. You can find a (not so) detailed ...
1
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1answer
68 views

Improving strategy to solve this constrained root-finding problem

I am looking for roots of the function eqs defined below. It has $2k$ unknowns and returns a vector of $2k-1$ components. The sole purpose of the following block ...
1
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0answers
62 views

Exponential Matrix Diffentiation

I have been struggling with the following question while solving an optimization problem in $\mathbb{R}_{+}^G$. Basically, I have $$\min_{y \in \mathbb{R}_{+}^G} F(y) = y^{T}\mathcal{K} + \exp(-y^{T} ...
0
votes
1answer
53 views

Minimization with respect to functional constraints [closed]

I am trying to do the following on Mathematica: Given a pair $(x,y)$, minimize an objective function $f(x,z)$ such that z satisfies $g(x,z) \leq g(x,y)$. I have defined both functions ...
1
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1answer
60 views

Count and NMinimize don't seem to work together

Initially I write down a 2x2 unitary (Uni) , make a tensor product 4 times (LocalUni) and apply it to an initial numerical matrix Rho, to obtain RhoLU, that depends on 12 parameters. This is my code: ...
0
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1answer
69 views

Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily ...
15
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1answer
321 views

Bug in plotting function using FindMinimum?

Bug introduced in 10.0 and persisting through 10.3 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of ...
3
votes
2answers
264 views

How to find the maximum of this function on the positive real line?

I need to maximize this function on the positive real line: $$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be ...
2
votes
1answer
152 views

Fitting to the system of equations with no analytical solution

I'm trying to fit linear combination of 2 functions to my experimental data set (it represents voltage of 2 photodiodes - Voc1 and Voc2 - connected in series under illumination - S) ...
4
votes
1answer
75 views

How to get function output with Manipulate

I have a program, which makes Gauss-Jordan transformations (not too pretty, I suppose). I want to get output with Manipulator like that: Two-Phase Simplex Method with only "step number" slider. One ...
7
votes
1answer
186 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
7
votes
3answers
243 views

Find parameters that minimize the distance between two curves in terms of the infinite norm

I am trying to implement a very simple NMinimize code that would search for parameters of a polynomial that minimize (globally) the distance between this polynomial ...
2
votes
2answers
89 views

None of the NMinimize methods leads to the answers of the equation

The following 10 equations has one set of exact answer using NSolve in Mathematica 9.0.0.0 (for positive c2, alpha1, alpha3, beta1, beta3, A1 and A3): ...
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2answers
83 views

Maxima turn out to be false maxima when extremising function locally

In short: I have a 2-D function that gives this plot, where the orange dots are maxima: There are 4 maxima in this plot. Now, I plot the function again in a smaller region, close to these maxima, ...
1
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1answer
98 views

Find function tracing the maximum of a 2D function

I'd like to solve the following problem: Given MI[o_, n_] := Log2[1 + 4 o (Sqrt@n + Sqrt[1 + n])^2] Find a function f[n_] ...
3
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1answer
307 views

Numerical Instability?

Current Status Please skip ahead to Update 2: the key questions are now: 1/ Why does Mma generally fail to find the minimum for a well behaved function when the function does not have infinite ...
0
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1answer
71 views

a question about Nminimize [closed]

I have 10 equations and 10 unknown parameters such as alpha1,alpha2,a1,a3,... which I want to find them by minimizing ...
6
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2answers
280 views

Graphically solving a linear programming problem

I try to realize the graphical linear programming method. Here is my code ...
0
votes
0answers
46 views

Incorporating sophisticated constraints on the approximating function into NMinimize

Following the approach as given in the answer of Belisarius here I just wonder how one could incorporate some more sophisticated requirements on the approximating function. Suppose the approximating ...
4
votes
2answers
160 views

FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)

I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize. In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
1
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1answer
51 views
2
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1answer
108 views

Maximum of the minimum of two functions

I have two functions, each with 15 variables. How can I find maximum (minimum) of these functions? I know that minimum (maximum) of two functions is a multi-criteria function but I cannot find it. ...
0
votes
1answer
56 views

Problem with inequality constraint

I'm using NMinimize to solve the following objective function. ...
0
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0answers
44 views

Minimize function with logical arguments

How can I minimize or maximize a function (even numerically) with logical arguments, taking only 0s and 1s, also with constraints? E.g. ...
3
votes
1answer
85 views

ArgMax, FindArgMax, and NArgMax disagreeing on answer

In working on an estimation problem, I created three Gaussian-like functions. The ML estimate could be seen as the argmax of the product of the three functions. In trying to get the code to run ...
2
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0answers
50 views

FindMinimum not accurate [closed]

Consider the function f[B_, d_] := -158.57189 + 982.533102 B^2 - 5.6768579 d + 895.1968 d^2 + B (-18.7772 + 655.02206 d); ...
4
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1answer
88 views
3
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1answer
134 views

How to make Maximize function successfully maximize in general?

Having looked at Maximize Documentation SO: Mathematica: Commands return no output, but itself. Bug? Problem with Maximize Why won't Mathematica Solve a set of two equations for one variable? ...
5
votes
2answers
100 views

Parallel function evaluation for minimal value

I am asking myself, if the evaluation of a function f looking for a minimal value over a discrete set of values can be parallelize (brute scan for a potential ...
1
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1answer
57 views

Trying to maximize an expression with integer and real variables

I am trying to solve this equation The link has a screen capture of the equation and the solution. I am looking for the values of a1 and a2 in particular, but they need to be real numbers. s1 and s2 ...
3
votes
2answers
97 views

Optimization not evaluating, further specifications?

I am trying to find the global minimum of this simple function for real x and y f = x^2*(1 + Sin[y]); Of course, I know it is 0. But Mathematica seems not be able to handle this expression since ...
1
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0answers
52 views
3
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1answer
90 views

Speeding up constrained optimization problem solving

I have a problem on my homework with Lagrangian multipliers that Mathematica has now been bashing at fruitlessly for 10 minutes. I'm not sure whether I did something horribly wrong codewise, but it's ...
4
votes
1answer
172 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
6
votes
1answer
368 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 ...