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

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1
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2answers
218 views

Need an efficient method for finding certain matrices

I am trying to write a function which produces square matrices with certain characteristics. The function should have two inputs: number of the rows, n number of ...
1
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1answer
139 views

Working precision for each variable

How can I define working precision for each variable individually for example: Maximize[x y< 100, {x, y}] where the working precisions for ...
0
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0answers
158 views

Non linear constrained interger Optimization

I need to maximize the equation below which is subjected to some nonlinear constraints Maximize hsum + isum + jsum + ksum + lsum + msum + nsum + osum ...
0
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1answer
357 views

Maximizing trig functions in Mathematica

Just to give some context, my motivation for this programming question is to understand the derivation of the CSHS inequality and basically entails maximizing the following function: ...
1
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2answers
285 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 ...
0
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0answers
58 views

NMinimize and FindRoot Issues with System of Equations [duplicate]

I am trying to solve a constrained optimization problem with a system of transcendental equations and am running into issues with NMinimize. I have a system of equations (...
1
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0answers
155 views

Conditional solution for system of linear equations

I have a linear equation system Q.m = t, with m unkown and where Q has dimensions ...
4
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1answer
326 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - ...
3
votes
0answers
166 views

Trouble with Minimize

Minimize[{t^2, 1 == 3*t + 16*u}, {t, u}, Integers] It does not give the solution t = -5 and u = 1. Am I missing something? The solution being known and ...
1
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1answer
172 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. ...
1
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1answer
412 views

using array elements in minimization

I have switched from mupad to Mathematica, however the syntax is completely different here. I want to ...
0
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0answers
69 views

Initializing Minimization [duplicate]

I am trying to implement a model predictive control scheme in Mathematica, e.g. I optimize input sequences by predicting future outputs. So every time I call the cost function it will simulate the ...
4
votes
1answer
198 views

How to solve this simple equation?

I want to minimize a quadratic equation, but Mathematica does not solve it and only rewrites the solution. I wonder if there exist any way I can skip the computation by hand (I can solve it using ...
3
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2answers
333 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). ...
1
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1answer
2k views

Using NonlinearModelFit to fit data with errors

Assume we have some data of measurements SeedRandom[9]; data = Table[{i,2*(1 + 5*RandomReal[])*Exp[-0.01*(1 + RandomReal[])*i]}, {i, {0, 100, 200, 400, 700}}]; ...
2
votes
0answers
193 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 ...
12
votes
2answers
667 views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
4
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0answers
523 views
2
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1answer
199 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 ...
4
votes
1answer
156 views

Minimize failing on a polynomial

Calling: Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2, 0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}] returns ...
5
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1answer
273 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
1
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1answer
207 views

List comparison in constraints for Minimize

I am trying to solve an optimization problem, a simplified version of which is as follows: ...
4
votes
3answers
428 views

How to find the minimum of this constrained expression?

Let $x$, $y$, $z$ be three nonegative real numbers and $x^2 + y^2 + z^2 = 5.$ Find the minimum of the expression $$E=\dfrac{1}{2}x^2 y^2 + y^2 z^2 + z^2 x^2 + \dfrac{96}{x + y + z + 1}.$$ I tried ...
3
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1answer
198 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
2
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1answer
290 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? ...
0
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1answer
983 views

How to find the global maximum of a function? [closed]

I tried the following but plotting the function clearly reveals that there is a global maximum around $r = 7$ (here $a = 0.53$) ...
1
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2answers
609 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 ...
2
votes
1answer
114 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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2answers
272 views

NMinimize problem again

Following up my previous question which got great replies, I am now trying to do ...
9
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4answers
2k views

NMinimize usage

I would like to minimize functions including the following. NMinimize[{1 - (1 - 1/n)^x - x/n, n > x, x > 1}, {n, x}] However Mathematica complains about ...
0
votes
1answer
176 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
0
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1answer
368 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 ...
7
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3answers
1k views

Travelling salesman with start and end points for 30 points

I am doing a route optimisation for delivery vehicles and failing dismally. Please see problem statement below. My current solution uses FindShortestTour, but this does not have defined start and end ...
2
votes
1answer
524 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 ...
13
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3answers
927 views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
0
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1answer
87 views
11
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1answer
2k views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
0
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0answers
427 views

Mathematica, nested optmization [duplicate]

I want to use the solution of Maximize, defined as a function, in another function. Here's an example: ...
3
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2answers
141 views

Find condition under which variables fall away

I have a somewhat lengthy expression, looking like expr = 1 + x + b + Pi + 2*a Is there some way of generating a relationship between ...
1
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0answers
128 views

How to express this output in the form $X=A.x$?

This problem arose in my stereo vision project. I have two matrices: $$ A = \left( \begin{array}{ccc} \text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & ...
36
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7answers
2k views

Character edge finding

The following line of code finds the edge of a character: ...
1
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1answer
148 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: ...
1
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1answer
511 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
1
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0answers
62 views

Using lists as optimization parameters [duplicate]

Possible Duplicate: Minimizing a function of many coordinates Suppose that the function $F[\vec{x}]$ computes a certain polynomial of the elements of the list $\vec{x}$. How can I use ...
2
votes
0answers
412 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, ...
2
votes
1answer
514 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
votes
3answers
2k 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 ...