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Questions tagged [mathematical-optimization]

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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2answers
1k views

Find the values of 3 variables that best fit 6 equations [duplicate]

I have 6 equations ...
2
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1answer
186 views

Simultaneous minimisation of chi-square

I have a series of data sets with which I would like to fit a model function to simultaneously. In each data set, I have coordinates $\left\{x,y\right\}$ and an error bar for $y$. The data sets are ...
2
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1answer
636 views

Why is `NMinimize` trying to evaluate my function analytically instead of numerically?

I have been having some trouble with NMinimize. I am trying NMinimize[f[x], x] where f is ...
2
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1answer
43 views

How to Add a Constraint on the Derivative of the Model in FindFit

I would like to add constraints on a model and its derivatives and then use FindFit to fit some parameters. An example is below: ...
2
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0answers
51 views

Using FindMinimum to solve equations as constraints

As suggested here, a system of equations can be seen as constraints in a minimization procedure with a zero cost function. For instance: ...
2
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1answer
131 views

Application of Maximize: The cuboid constrained to the ellipsoid in $\mathbb{R}^3$

Since I am a student of Mathematics I enjoy to apply MMA to problems that I have a solid understanding in. The following would be such a problem: Maximize $f: \mathbb{R}^3 \to \mathbb{R}$ given by $...
2
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2answers
168 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 ...
2
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2answers
476 views

Minimize loop optimization

I'm new in Mathematica 10. So far, I have a two variable-function and I've use Minimize to find the optimal solution. Nevertheless, I'd like to make a sensibility analysis and study how this optimal ...
2
votes
1answer
128 views

Maximax optimization over a particular matrix

I have the summation of $N$ matrices which are weighted by some weighing factors (parameters): $$M_\alpha=\sum_{i=1}^N \alpha_i M_i$$ $$d_{\alpha}=\arg\max_{rows} M_\alpha$$ The ideal vector $d$ is ...
2
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1answer
803 views

How to Minimize a 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 ...
2
votes
5answers
140 views

How can I find the $c$ such $Max[Fibonacci[Range[c]]] = 13$?

How can I find the $c$ such Max[Fibonacci[Range[c]]] = 13 I tried Reduce but there is an error message ...
2
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1answer
251 views

Step Monitor option in DifferentialEvolution

Using the "Step Monitor" option what exactly do I read? Does it show me the "best solution" for each population? Or does it show me each search point in the population? Also is there an integrated "...
1
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1answer
479 views

Solving coupled PDE and ODE

I want to solve a system of partial differential equation in mathematica. equation is: $y0=0.5 t0=30 λ_12=0.3 λ_13=λ_23=0.01 λ_21=2.8$ I am new in mathematica. please help me for solving ...
1
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1answer
85 views

`Maximize` is running forever

I'm trying to maximize the following function $f$ with respect to $r$ and $k$: $f=\frac{d^3+3 d^2 (k (r-1)-s)+3 d \left(k^2 ((r-3) r+1)+2 k r s-2 (r-1) s^2\right)+k^3 (r ((r-1) r+3)-1)-3 k^2 r^2 s+3 (...
1
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3answers
101 views

3D Plot the result of local Minimize with varying parameter values

I'm faced with the following minimization problem: Find $r\in[0,1]$ that minimizes $\frac{d^2+k^2 (1-2r)r}{2(1-r)r}$, which is bounded by 0 and 1. In addition, $k<d$ holds and each of $d$ and $k$ ...
1
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1answer
175 views

What is wrong with my ArgMin expression?

I need to find the minimum of a function $mj_1^2+mj_2^2$ where my $mj$ are constrained. I wrote this expression: ...
1
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2answers
905 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
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1answer
225 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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1answer
153 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my problem)...
1
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0answers
98 views

What are the differences between these functions when used for NMaximize?

In short, the question is how to construct the function you want to optimize? ...
1
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1answer
62 views

3D Plot multiple maximization results in one same diagram

My objective function, $f(r,k;s,d)$, takes three different expressions, denoted by $f^1$, $f^2$, and $f^3$, respecitvely, depending on the conditions for the arguments and parameters as follows: $f^1(...
0
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1answer
99 views

Finding the right DeleteCases pattern for <<199>>

I have a list in Mathematica with several items like <<199>> and <<104>>, I would like to get rid of them using DeleteCases, but none of the patterns I ...
0
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1answer
251 views

Variable integration limits over real numbers only [closed]

I have a simple question regarding this code: ...
0
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0answers
112 views

Linear programming pivot

Here my object is purely pedagogical. When I was a student I hated linear programming because of the numerous operation we have to solve the simplest linear program. So now that I teach linear ...
0
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2answers
135 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 ...
0
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1answer
103 views

About nonstandard evaluation

I'd like to do some tedious calculations. The toy model is something like: ...
0
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1answer
30 views

How to have NonlinearModelFit not evaluate a function too early?

This is a follow up of my previous question How can I define the following function for arbitray values of the arguments? that received no attention so here I will try to be more concise with the ...
0
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1answer
63 views

Find roots of a polynomial equation or simplify

I have an equation like below: ...
0
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0answers
55 views

Evaluating multiple lines of code inside a Do loop and extracting results

I'm trying to use NMaximize to maximize a function within a looped domain, and evaluate several different expressions at each of those solutions. What I'd like to ...
0
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1answer
221 views

optimization problem with NDSolve and Import cannot get any results, even without error message

I want to minimize the function ff. When ff is calculated for a specified point the answer is correct: ...
0
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1answer
45 views

Give Mathematica points in the XY plane and find equation that generates them

I am finding the minima of a 2D cubic periodic function by "brute force", i.e. looking for the (x,y) positions where the both the x and y derivatives are 0. This returns a list of points, in this ...
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5answers
197 views

Find optimal integer solution to linear equation (Wolfram Alpha)

I'm sorry if this is potentially off topic, but I posted this question at the Math SE and they pointed me here. Both SE sites have a tag for Wolfram Alpha, but maybe you guys are better equipped to ...
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0answers
69 views

How to obtain all minima? [duplicate]

If you Solve an equation, you obtain all solutions. But If you NMinimize a function, you only get one minimum. The question is:...
0
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1answer
104 views

Minimizing a function problem

I'm solving an elastoplastic problem of the Ducker Prager model using the closest point projection method, which consists of minimizing a distance between a trial stress and the yield surface in the ...
0
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1answer
41 views

ListPlot3D for optimization with varying parameter values

This is a followup question from Alex Trounev's answer to my question in the following post: 3D-Plot optimization results for varying parameter values Consider my objective function, objF: ...
0
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1answer
900 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
0
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1answer
50 views

Maximize a definite integral with constraints on the limits

I would like to maximize the following definite double integral with respect to $0<r<\frac{1}{2}$: $\int _0^{\frac{d}{1-r}}\int _{\frac{d+r x-x}{r}}^s [(1-r) x+r y -d]dydx$ under the ...
0
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1answer
35 views

Nested optimization problem 3

thanks to Ulrich Neumann I am getting close to the solution of my problem... However, Mathematica tells me that no points satisfy the constraints of the following problem: ...
0
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2answers
436 views

Lagrange multipliers code runs forever

I am writing a code for a Lagrange multipliers problem with three variables. My code looks like this: ...
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1answer
77 views

Optimization problem [closed]

I have the following function ...