Questions tagged [mathematical-optimization]

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

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12
votes
1answer
1k views

Fitting Vogel's formula for phyllotaxis to the image of a flower

After having read this question I was inspired to investigate how we could take an image of a plant displaying phyllotaxis and fit Vogel's model of phyllotaxis to the image. The theory is very simple. ...
2
votes
1answer
167 views

Declaration of variables in large Linear Programming model with NMaximize

I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem: $$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\ s.t\quad \...
3
votes
1answer
201 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ &...
6
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0answers
202 views

Issue with FindCurvePath

I have a problem with the function FindCurvePath. In some cases it crashes the Mathematica 9 Kernel. Here an example, where it crashes the kernel: ...
1
vote
1answer
283 views

NMinimize stops with no more memory?

I am using NMinimize function for simulation based optimization. So my objective function is a simulation that runs for every combination of variable values evaluated by NMinimize function. However, ...
4
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1answer
854 views

Arnold's problem #8

The famous Arnold's problems (see http://www.math.upenn.edu/Arnold/Arnold-Trivium-1991.pdf ) are aimed at the strong graduate and postgraduate students of the top universities. I find it remarkable ...
27
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2answers
6k views

Optimization of a portfolio of stocks

I would like to use Mathematica to perform an optimization of a portfolio composed by 10 stocks. I did the first part to compute yields and expected yields, but I don't know how to finish the ...
4
votes
1answer
565 views

Ordinary differential equation invloving the function composition

I want to solve the following function: DSolve[(A1*Exp[B1*f[x]] + A2*Exp[B2*f[x]])*f'[x] == A1*Exp[B1*x] + A2*Exp[B2*x], f[x], x] And this is what I get as an ...
1
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0answers
470 views

Minimizing a functional takes forever

I need help with minimizing a functional in Mathematica. I have a function $V(\xi)=\sum_{i=1}^\infty C_{3_i}J_0(\xi/C_i)+C_{4_i}Y_0(\xi/C_i),~~~\Sigma\leq\xi\leq\xi_1$, and want to find such $\{C_{...
5
votes
1answer
1k views

Fitting one function to another

I'd like to see how close I can fit an exponential function to a cosine function in the domain of $\;-\frac{\pi}{2}$ to $\frac{\pi}{2}$ in the least squares sense. ...
-1
votes
3answers
6k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
2
votes
1answer
639 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 ...
5
votes
2answers
192 views

Finding the maximal `t` at which `u[x,t] == 1`?

Given the smooth function u[x,t] on a domain, how do I find the maximal t at which ...
4
votes
1answer
654 views

FindMaximum of loglikelihood in Gaussian Process

I am trying to implement a Gaussian Process and have problems to maximize the loglikelihood because the function consists of a determinant of a matrix that is dependent of 2 variables and the product ...
2
votes
1answer
1k views

FindMinimum produces error message

I'm trying to solve a logistic regression problem using Mathematica -- more to improve my Mathematica skills than to solve the problem as I have already solved it using Octave. The problem I am ...
20
votes
3answers
9k 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 ...
3
votes
0answers
331 views

Optimization with Matrix value constraint

I am trying to find the orientation and position of a polygon resting on a curved surface under gravity.The polygon MUST not be penetrated by any part of the surface below. Here is an example for a ...
3
votes
1answer
697 views

How can I set constraints on parameters in NelderMeadMinimize package?

I read about NelderMeadMinimize package. How can I set constraints on the parameters? For example I want to minimize an equation with $10$ parameters such as ${a_1, a_2, ....}$. I want to put the ...
7
votes
2answers
217 views

How to Maximize[Log[n]^(1/Log[n]), n]

I am new to Mathematica and am trying to work out how to use Maximize. Maximize[Log[n]^(1/Log[n]),n] Should give a solution at $e^e$. However in Mathematica you ...
12
votes
1answer
3k 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
1answer
1k views

Find maximum from NDSolve output

Here is my code: ...
1
vote
1answer
186 views

Bound on number of function evalulations in FindMinimum

I am minimizing a nonlinear constrained problem using FindMinimum. The problem involves about 200 variables and the function is a black-box which cannot be compiled/...
4
votes
1answer
280 views

Forcing optimal solution for FindShortestTour

I use FindShortestTour as explained here and it works nicely for a small number of cities. However when I try this with as little as 16 cities, the given tour isn't ...
2
votes
1answer
161 views

LinearProgramming errors

I have a family of equations I want to solve over the non-negative integers. One particular instance of it is this. ...
4
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0answers
278 views

Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem) [duplicate]

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
7
votes
1answer
527 views

Visualization of iteration procedure in NMinimize

I have this optimization code: ...
2
votes
1answer
1k views

Simulated Annealing InitialPoints option

I have a cost function that depends on 4 parameters: CostFunction[{tx,ty,tz,ox}]. I used NMinimize[] function with ...
1
vote
1answer
583 views

No Speedup Compiled Function in FindMinimum

The problem: I would like to minimize an objective function with respect to 12 variables. Minimization should be executed as fast as possible. Compiling the objective function increases the execution ...
2
votes
1answer
1k views

FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
0
votes
0answers
53 views

How to manipulate lists to get only part of the value [duplicate]

This is really a question about manipulating the output of Maximize. I have a function of 2 variables, defined thus: ...
1
vote
1answer
172 views

Plot3D and NMinimize do not work correctly?

See my code: ...
2
votes
2answers
304 views

Nonlinear Optimization with conditional statement

I find Maximize doesn't work well under conditional statement. Here is an example. A car is driving up a slope. I want to find out the largest slope angle the car can drive upwards. I choose the ...
10
votes
4answers
925 views

Finding a point from a set of contours such that it is nearest to a given point

I have several contour lines and one point. How can I find a point in one of those contour lines which is nearest to the given point? ...
5
votes
2answers
419 views

Optimum number of cog teeth for two step helical gearbox

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I. I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
4
votes
1answer
113 views

quadratic constraint feasibility

Suppose that $A$ is an $n \times n$ matrix, and I have observed some entries of $A$, say, $A_S$ ($A$ restricted on $S$) for some subset $S$ in $\{1,...,n\} \times \{1,...,n\}$. I want to know if it's ...
14
votes
1answer
2k views

ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
1
vote
1answer
168 views

Minimum value with two factors

Approximate the minimum value of $2e^{x-2}-6x+xe^{x-2}$. Is my input correct? If not can you please correct it? ...
2
votes
1answer
678 views

Maximize over permutations

I have a set $S=\{s_1,\ldots,s_k\}$ and would like to maximize a fixed expression over permutations of $S$: $\max f(x_1,\ldots,x_k)$ with $x_i\in S$ and $x_i=x_j\Rightarrow i=j$. Is there a ...
3
votes
2answers
1k views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
8
votes
3answers
2k views

Cannot find the maximum value of a function

Consider the following function: $a Sin(x)+b Cos(x)$ I tried to obtain the maximum value of this function using MaxValue[]: ...
1
vote
1answer
168 views

Function optimization errors

I have the following Mathematica code (Mathematica version 9): ...
8
votes
2answers
844 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 ...
2
votes
1answer
557 views

Linear Integer Programming with absolute values in objective function

I'm trying to solve a problem of the form $$ \left|a_{1,0}+a_{1,1} x_1 + a_{1,2}x_2\right| + \left|a_{2,0}+a_{2,1} x_1 + a_{2,2}x_2\right|\to\min, $$ where $a_{i,j}$ are real-valued coefficients and ...
11
votes
4answers
215 views

Constraint syntax compaction

Is there a more compact way to represent these constraints: NMaximize[{a+b+c,a <= 5 && b <= 5 && c <= 5...
6
votes
1answer
2k views

Packing squares into a circle

I am currently trying to solve and understand a problem about packing the maximum of squares into a circle. What I am trying to do, is to calculate the maximum number of variable sized squares (with ...
1
vote
1answer
542 views

A problem on generating convex hull

For example, I typed the following: ...
1
vote
1answer
673 views

NMaximize problem

Could anybody explain to me why the following code fails ? ...
2
votes
1answer
388 views

NMaximize and Conditional Loop

I have developed the following code that simulates a process that decays over time and then returns to its initial state periodically. When I pass a list of random integers in the interval $(1,0)$ as ...
1
vote
2answers
921 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in \mathbb{Z}_q^...
10
votes
2answers
4k views

Linear programming with many variables and parameters

I am trying to reconstruct the answer that is given in this report. (page 153 in Appendix B; Section B.2.1). They are given variables, parameters, constraints, and the objective function to minimize. ...