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
65 views

Techniques to find all local minima of black box function with n continuous derivatives?

I have a blackbox function f on [a,b] that is known to be continuous, and has n continuous derivatives. The function uses polynomial interpolations (but isn't a polynomial interpolation itself), so no ...
3
votes
2answers
72 views

Maximizing a function defined using NIntegrate [duplicate]

I have two functions fn[x,y,z] which is in integral form and I have another function gn[x,y] which is also in integral form ...
6
votes
2answers
341 views

How to find valleys of data using new function in V10 PeakDetect

One of the great new function in V10 is PeakDetect. It can detect peaks according to desired sharpness as shown in this example: ...
0
votes
0answers
30 views

Nested optimization (in a dynamic game) [on hold]

I have a dynamic game in two stages with two players. The solution of this game requires first to find the Nash equilibrium in stage 1 with correct expectations of the decisions taken at stage 2. At ...
0
votes
0answers
110 views

Linear interpolation over 2 variables [duplicate]

I'm tuning a function to data over 4-5 variables using Differential Evolution. The objective function calls frequently interpolation function. I came to a point, where compiling the objective function ...
8
votes
1answer
104 views

FindMaximum failing on a trivial problem [on hold]

I am trying to solve a trivial optimization problem with FindMaximum but for some reason it is not going. I reduced the problem down to the following non-working ...
0
votes
1answer
32 views

Calculate Max-Min value and corresponding parameters

I have two functions funA and funB which are also functions a,b,x,and ...
0
votes
1answer
332 views

Finding resolution of an optical system using Rayleigh criterion

I want to use the Rayleigh criterion to find the resolution of an optical system. I have two functions f1 = Sinc[x]^2 and ...
2
votes
1answer
33 views

Numerical functions as constraints for NMaximize

I want to use NMaximize to solve a problem like this: $\quad \quad \max_y f(y) \text{ subject to } \max_x g(x, y) \leq c.$ Rather than reproduce my (messier) ...
4
votes
1answer
260 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
3
votes
1answer
37 views
6
votes
1answer
876 views

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 ...
4
votes
2answers
174 views

Maximization in Mathematica using matrix and vector notation

I am trying to solve a simple maximization problem in Mathematica, using matrix and vector notation. ...
6
votes
1answer
342 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 ...
3
votes
1answer
231 views

Simulating an optimization problem

I have an optimization problem like below: $\text{minimize } - \sum_k w_k \log r_k$ $ a \leq r_k \leq b_k, k = 1, \cdots, 10$ Here, $w $ and $b$ is a set of constant: $w = [w_1, \cdots, w_{10}]$ ...
1
vote
0answers
35 views

Solving a Nonlinear Optimization using Primal-Dual Interior point method [closed]

I want to solve an optimization problem using the Primal-Dual Interior Point Method. Although Mathematica gives the result directly when I use the command ...
1
vote
0answers
32 views

Linear Programming Using Dual Simplex method

I want to solve an optimization problem using the Dual Simplex Method. Although Mathematica gives the result directly when I use the command Minimize but I want to ...
2
votes
0answers
50 views

FindMinimum pre-conditioning

I am wondering about what kind of pre-conditioning FindMinimum performs on the user specified function (to be minimized) before the actual minimization starts, and ...
1
vote
1answer
515 views

FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
2
votes
1answer
66 views

How to find the local minimum points in the multi-dimensional numerical data?

I am trying to get some local minima of an n-dimensional function (which only has numerical form). For two-dimensional function data, we can find the local minimum points from the contour plot easily. ...
1
vote
0answers
25 views

Minimizing values of expressions dependent on more variables [closed]

I need to enforce seven expressions dependent on seven variables to be zero. However, the expressions are quite complicated and generaly I get a system of transcendental equations which only sometimes ...
3
votes
1answer
84 views

Sparse Hessian for FindMinimum? Broken?

Is the sparse Hessian mechanism for FindMinimum[] (Method->"Newton") broken? Or am I simply not apprehending its proper setup? Here's what's happening. Below is for solving the example problem ...
0
votes
1answer
100 views

FindMinimum runs out of Memory

I have a function which runs fine when I evaluate it. However, when I try to find its optimal parameters using FindMinimum it quickly consumes all available memory ...
1
vote
1answer
58 views

How to Minimize a Log/Linear function symbolically?

I have my objective function as : $\hspace{25mm} \text{Minimize} \sum_k- \alpha_k \log_2 W_k$ $\hspace{25mm} \text{subject to}: 0\leq W_k \leq q', 0 \leq \alpha_k \leq 1 $ $\hspace{25mm} k ...
4
votes
2answers
246 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
1
vote
2answers
115 views

Doing same operation on multiple files

Is there a way in mathematica to do same operation on multiple files at once? And preferably have the output in a table or list form? I want to do the following operation preferably in few non-labor ...
0
votes
0answers
38 views

Simplifying sums of rational trigonometric functions

After simplifying the trigonometric functions as advised before (cf. Simplifying Expressions for FindMinimum), I obtained a sum of 62 similar expressions, the first three as in the below: ...
2
votes
1answer
105 views

Solve overdetermined set using Mathematica?

As shown below, this is a overdetermined system. Could you teach me how to find the optimized solution in Mathematica? I know it could be solved by the method of least square, but how to realize it in ...
3
votes
2answers
61 views

FindMinimum[] complains about values outside its constraints

The following optimization has a constraint that b<0, but it's failing because the integral diverges when it tries a small positive b. ...
4
votes
0answers
113 views

Visualizing the Lagrange Multiplier Solution

This question is based on work in Susan Colley's Vector Calculus, 4th ed. The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint ...
5
votes
3answers
200 views

Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...
1
vote
1answer
47 views

How to repeatly use random number generator in optimization problem

I am looking to run the optimization problem. I already finish my optimization code as below. ...
4
votes
1answer
78 views

Simple minimization not evaluating

I tried to solve a rather simple optimization problem, which Mathematica apparently cannot handle. A minimal example is the following: ...
0
votes
1answer
153 views

Mathematica won't maximize my function

I am trying to maximize two functions. For the first one, the code runs correctly and returns the desired answer: ...
0
votes
0answers
52 views

Maximizing a 3-variable function

I want to find the maximum of the following function $$f(x,y,z) := -y^2 - 3 z^2 + xy + 2xz - 2yz + my + (m + n + t)z - nx,$$ where $m,n,t$ are indeterminate constants, subject to the constraints ...
0
votes
0answers
79 views

NIntegrate Polynomial of high degree

I want to integrate a polynomial of degree 100 and higher over a domain that is the intersection of two balls like ...
0
votes
0answers
49 views

Solving matrix optimization

I have the following problem. Let $X_1, X_2, \cdots, X_k$ are $n \times n$ Hermitian matrices (need not be positive) given. Let a $n \times n$ positive matrix $A$ is given such that $Tr(A.X_j)<0$ ...
2
votes
1answer
79 views

Simplifying Expressions for FindMinimum

I am currently trying to apply the FindMinimum function to find the lowest energy of an expression. My current expression as of now is relatively complicated. It is the summation of 48 similar terms, ...
6
votes
1answer
148 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
1
vote
2answers
236 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 ...
11
votes
0answers
214 views

Bug in plotting function using FindMinimum?

Bug introduced in 10.0 and persisting through 10.2 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of ...
4
votes
1answer
126 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, ...
4
votes
1answer
295 views

Maximizing functions with Which statements

I'd like to be able to find the maximum value that my Capex function (see below) generates. This is a fairly simple function so I could just add it up but I have more complex functions of a similar ...
2
votes
1answer
126 views

NMaximize and Accuracy

I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
19
votes
2answers
388 views

Maximize[Cos[x - 1], x] is not evaluated

No explanation needed: Maximize[Cos[x + 1], x] Maximize[Cos[x - 1], x] producing ...
8
votes
2answers
142 views

Efficient solution for a discrete assignment problem with pairwise costs

Let's consider a simple graph with N vertices, and a corresponding set of N items. The goal of the problem is to assign every item to a vertex on the graph so that sum of a per-edge (that is ...
0
votes
1answer
31 views

How can I name to a saved file with the numerical values of some specific parameters? [duplicate]

I'm using some parameters to determine the elements of a list. I want to save this list with DumpSave, but I need to name it with its parameters. For example, I use the following parameters ...