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

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1answer
342 views

Problem using the DifferentialEvolution method of NMinimize [closed]

I have a function of 20 parameters, which 3 of the parameters are my physical parameters, and the others are pull terms to fix the errors. The goal is finding the global minimum of this function, to ...
2
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1answer
319 views

Restrictions problem

I tried to program a simple linear optimization model and don't know where my mistake lies. The function should be a sum over "t" and "z" from the product of two constants ("e" and "H") and the ...
2
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1answer
132 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
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1answer
236 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 ...
2
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2answers
142 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 ...
2
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2answers
212 views

Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
2
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1answer
152 views

How can I change the MPS format in Linear Programming samples of Mathematica?

I am trying to play with some linear programming examples of Mathematica as ExampleData[{"LinearProgramming", "blend"}, "Equations"]. It gives me the MPS format of ...
2
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1answer
301 views

FindMinimum, NMinimize, etc. with external process

I was hoping to be able to use MMA's minimization power to work with an external process. I want to minimize the function 'TryThisNumber[x_]' which sends the value of x to something external and gets ...
2
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1answer
237 views

Finding a fixed vector which minimizes the pairwise distance between noisy elements in two unordered arrays

Let $A$ and $B$ be two sets of $d$-dimensional coordinates of comparible (though not necessarily equal length). For example, here we can set $d = 3$ and have normalized values like: ...
2
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1answer
407 views

Problems with FindMinimum for Constrained Optimization

I am trying to define a simple optimization problem, arising from the discretization of a simple Optimal Control problem. The problem that results is essentially linear, with bilinearities only ...
2
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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 ...
2
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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 ...
2
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1answer
156 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 ...
2
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1answer
102 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
2
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1answer
243 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
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0answers
48 views

How to reduce notebook or CDF file size with many images in it? [duplicate]

We love to use Mathematica notebooks to keep our notes, so we import lot of scanned photos into notebooks. However, the nb file size goes crazy large after importing photos in it. For example, ...
2
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0answers
65 views

Simulated Annealing Parameters and Results

I am using SimulatedAnnealing method for a simulation based optimization problem and was wondering if someone can enlighten me on the following features: Is there ...
2
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0answers
150 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 ...
2
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0answers
122 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
2
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0answers
269 views

Why my Mathematica 9.0.1 wont work with some samples of Mathematica in Graph Theory?

I updated my Mathematica recently to 9.0.1 cause the previous version was giving me freaky result especially in FindMinimumCostFlow and ...
2
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0answers
287 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
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0answers
251 views

Having difficulty with the Minimize command

I am having trouble getting an answer to this question...Am I missing something that anybody can see. ...
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2answers
106 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 ...
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1answer
556 views

How to find local minima of a multivariate function with singularity?

I am working on a logistic regression problem which requires minimizing a cost function J[{theta0, theta1, theta2}, X, y] to find the optimal value for fitting ...
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1answer
164 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 ...
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2answers
465 views

Area of the largest rectangle bounded by $y=x^2$ and the x-axis within the unit interval

I am trying to find the area of the largest rectangle (whose sides are parallel to the coordinate axes) contained in the region bounded by the graphs of $y = 0, y = x^2,$ and $x = 1$ using ...
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3answers
1k views

Determining the local extrema of discrete data [duplicate]

Possible Duplicate: Local max/min of Mathematica data sets If I have a continuous function f (for example ...
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3answers
187 views

How to find maximum ConditionalExpression among all solutions

For example I want to find solution with maximum value among solutions (and possibly plot it): ...
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2answers
170 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 ...
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1answer
120 views

Feasibility of Linear Program

I have a set of (real) linear equations/inequalities and I want to know whether they have a solution, and to find at least one. The goal is to do this quickly. ...
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1answer
202 views

Understanding execution time in nested loops

I have the following simple code ...
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2answers
293 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 ...
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2answers
219 views

Finding normals to a curve through a given point

I want to find x on curve $y(x)$, where curve $y(x)$ is perpendicular to point $(x_0,y_0)$. for this I minimize the distance between points $(x,y(x))$ and $(x_0,y_0)$, here's an example for point ...
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1answer
149 views

How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? ...
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1answer
139 views

Seemingly simple optimization problem is slow

I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so: ...
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2answers
166 views

Scalar product of two vectors have the least value

In geometry 3D, let $A(1,2,-3) $ and $B(-1,4,1)$ are two points. In the plane $(P):2x-3y+3z-17=0$, find a point $M$ such that the scalar product of two vectors $AM$ and $BM$ will have the least value. ...
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2answers
1k views

Find the dimensions of a cylindrical can that will minimize the cost of the material

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. This is a standard calculus problem. The volume of the ...
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2answers
69 views

Minimizing the maximal residual in mathematica

With this: d1 = 10; d2 = 4; mat = RandomReal[{-1, 1}, {d1, d2}]; vec = RandomReal[{-1, 1}, d1]; LeastSquares[mat, vec] ...
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1answer
131 views
1
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1answer
204 views

using array elements in minimization

I have switched from mupad to Mathematica, however the syntax is completely different here. I want to ...
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1answer
48 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 *) ...
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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 & & \\ ...
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1answer
216 views
1
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1answer
108 views

Finding exact local extrema of simple functions

I want to exactly find all the local maxima of f[x_] := x^4/4 - x^2/2 over the interval [-Sqrt[2], 1 + Pi/10]. The correct ...
1
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1answer
70 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 ...
1
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1answer
187 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 ...
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1answer
103 views

Numerical saddle point problem of a function of many variables

I want to find the following saddle point of the function of 10 variables: . I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
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1answer
110 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
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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 ...
1
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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? ...