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

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0
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2answers
104 views

Is it possible to monitor the sum of squared errors in a NonlinearModelFit or FindFit procedure during the process?

Since fitting procedures using NonlinearModelFit (or `FindFit) sometimes take very long, I would like to monitor the sum of squared errors during the process ...
4
votes
1answer
122 views

Mathematica Library

I created a Mathematica packagr and then I used the Needs function to add the library to my .nb file, but when use a function in my .nb file and the function is built in my library it comes up with ...
3
votes
1answer
217 views

$L_\infty$ norm minimization

I write supplemental explanation to render my aim of optimization. First Consider discrete time linear system below: \begin{equation} G(z)=\frac{1-e^{-0.3T}}{z^{100}(z-e^{-0.3T})} \end{equation} ...
1
vote
1answer
110 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
15
votes
2answers
356 views

Schedule programing problem with integer linear programming

I know how to model this question on paper, but I don't know how doing it in Mathematica. Imagine , there is a university student who want to choose courses for this semester and he got the ...
0
votes
0answers
44 views

Compiling Visual Studio C++ to Run on Computers without Mathematica [duplicate]

I have written a console application on Visual Studio C++ as below ...
8
votes
3answers
225 views

How can I complete a correlation matrix with missing values?

I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
1
vote
1answer
46 views

How to obtain dual values? in Simplex(LinearProg.) and… the final tableau? [closed]

I can resolve the function value and the primal values in Linear Programming like in (* Examen de avións Sept 2003 *) ...
5
votes
1answer
167 views

Fitting Vogner'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 Vogner's model of phyllotaxis to the image. The theory is very ...
2
votes
1answer
86 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 ...
8
votes
3answers
859 views

Which ColorFunction should I use to get such a gradient of blue-cyan-green-yellow-orange-red?

I want to get the effect in the above Figure. Here is my code: ...
1
vote
1answer
108 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 & & \\ ...
5
votes
0answers
130 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: ...
0
votes
1answer
107 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, ...
2
votes
1answer
514 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 ...
1
vote
2answers
167 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 ...
-3
votes
2answers
528 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
114 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
78 views

how to do variation

I have an equation needs to do variation. I can do it by hand, but I get different result by mathematica. maybe I made some mistakes in programming. can anyone point out for me? thanks This is how I ...
1
vote
0answers
79 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
127 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. ...
0
votes
0answers
123 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
474 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. ...
1
vote
1answer
102 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
155 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 ...
2
votes
1answer
130 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 ...
0
votes
1answer
169 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
154 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
149 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 ...
6
votes
2answers
126 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
160 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 ...
4
votes
1answer
132 views
1
vote
1answer
68 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
1answer
103 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
0answers
149 views

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

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
141 views

Visualization of iteration procedure in NMinimize

I have this optimization code: ...
2
votes
1answer
232 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
61 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 ...
0
votes
1answer
95 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 ...
0
votes
1answer
141 views

FindMinimum [] methods

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
0
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0answers
39 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
130 views
2
votes
2answers
141 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 ...
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
266 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 ...
3
votes
1answer
73 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
291 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
135 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
135 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
361 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...