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

learn more… | top users | synonyms (2)

3
votes
2answers
1k 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 ...
0
votes
0answers
199 views

FindMaxValue vs FindMaximum

I'm studyng the maximum value of the following function ...
8
votes
3answers
990 views
2
votes
1answer
123 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 & & \\ ...
1
vote
2answers
218 views

What's the best way to generate all the upper triangular matrix whose singular values are given?

For example, given $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what's the best way to generate all the upper triangular matrix ($3\times 3$) whose singular values are $\lambda_i$? Note:Given a ...
2
votes
1answer
568 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 ...
4
votes
1answer
153 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
vote
0answers
112 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 ...
3
votes
1answer
179 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. ...
4
votes
1answer
1k views

Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
0
votes
0answers
157 views

How minimize a function involving abs $(|\ldots|)$?

I am trying to decide the best way to solve this: Minimise $Y = | K + ax^2 + bxy + cy^2 |$, with decision variables $x$ and $y$ and $a > 0$. I also have a number of convex and affine ...
-1
votes
3answers
1k 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
192 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 ...
1
vote
1answer
148 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 ...
4
votes
2answers
162 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 ...
0
votes
1answer
289 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 ...
3
votes
0answers
186 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 ...
6
votes
2answers
140 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 ...
1
vote
1answer
412 views

Which methods are available for NMinimize? [closed]

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 ...
1
vote
1answer
94 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 ...
4
votes
0answers
201 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 ...
4
votes
1answer
200 views
2
votes
1answer
389 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
0answers
80 views

NMinimize memory consumption problem in Mathematica 9 vs. 7 & 8

I am having trouble using NMinimize in Mathematica 9 - Memory consumption overflows. The same NMinimize command, with the same ...
1
vote
1answer
154 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 ...
1
vote
1answer
241 views

FindMinimum [] methods

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
0
votes
0answers
43 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: ...
0
votes
0answers
41 views

How to fit ODE's coefficient, just like using NMinimize [duplicate]

I want to fit ODE's coefficients to a model. I tried using NMinimize, but it seems it does symbolic instead of numerical calculations. ...
5
votes
2answers
297 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 ...
2
votes
1answer
218 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 ...
3
votes
1answer
76 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 ...
9
votes
1answer
369 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
141 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? ...
1
vote
1answer
162 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 ...
2
votes
2answers
502 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
5
votes
1answer
422 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 ...
18
votes
2answers
710 views

Optimization with assumptions

I have the following problem, when I am trying to optimize function with pre-defined assumptions. I am using Mathematica 8 and I wrote the following simple code ...
7
votes
3answers
450 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
121 views

Function optimization errors

I have the following Mathematica code (Mathematica version 9): ...
1
vote
1answer
221 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
192 views

Constraint syntax compaction

Is there a more compact way to represent these constraints: NMaximize[{a+b+c,...
0
votes
1answer
206 views
1
vote
1answer
263 views

NMaximize problem

Could anybody explain to me why the following code fails ? ...
1
vote
2answers
334 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 ...
0
votes
1answer
98 views

Random variation inside NMaximize

I am using NMaximize as following code. ...
9
votes
1answer
815 views

Multi-objective genetic algorithm in Mathematica?

Is there any implementation of a multi-objective genetic algorithm for Mathematica?
0
votes
0answers
94 views

Inconsistent results in fits from NArgMin

EDIT: Just realized I had misspelled "inconsistent." I'm using version 7.0. I'm trying to fit a (noisy) data set to a large-order polynomial. (Just for context: there isn't a model for the ...
7
votes
1answer
1k views

Minimization by Nelder-Mead

Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...