I am trying to translate an Excel Solver problem (which solves correctly) into R code. I am aware that there is an array of packages allowing to solve constrained optimisation problems, but I still have not found one being able to formulate my problem and solve it.
The problem is the following
min sum(x)
s.t.:
g(f(x)) > 0.9
where:
x is a vector of boolean parameters to be identified
f(x) = x+4
g(f(x)) = SUMIF(f(x), "<90", M)/1000
M is a vector of constant terms with length equal to the lenght of the parameters of X.
In words, the problem aims at minimising the objective function sum(x). Here, x is the vector of boolean parameters the value of which must be determined, f(x) is a function which sums 4 to each parameter, and g(f(x)) is the conditional (to the value of each corresponding f(x)) sum of the vector of constant terms M.
I struggle to set up the problem with every constrained optimisation R package I have found. Is this problem solvable in R in the first place? If so, how?
Related
I am trying to solve two equations below for my project. I was unable to find any straightforward guide to solving the differential equations.
I am trying to plot a graph of h over time for the equations with a given initial h, miu, r, theta, g, L, and derivatives of h and theta wrt t. Is this possible? And if so, how?
The two equations mentioned
I tried to type the equations into Octave with the given conditions, but there seems to be an error that I am unable to identify.
Whatever is the numerical software you will use, Octave or another one (that does not formal calculation), the first step is to transform your system or N coupled Ordinary Differential Equations (ODEs) of order p into a system of p*N coupled ODEs of order 1.
This is always done by setting intermediate derivatives as new variables.
For your system, then
will become
Then, with Octave, and as explained in doc lsode you define a function say Xdot = dsys(X), that codes this system. X is the vector [h, theta, H, J], and Xdot is the returned vector of their respective derivatives, as defined by the right hand expressions of the system of first order ODEs.
So, the 2 first elements of Xdot will be trivial, just Xdot=[X(3) X(4) ...].
Of course, dsys() must also use the parameters M, g, m, ยต, L, and r. As far as i understand, they can't be passed as additional arguments to dsys(). So you must defined them before calling lsode.
For initial states, you must define the vector X0=[h0, theta0, H0, J0] of known initial values.
The vector of increasing times >= 0 to which you want to compute and get the values of X must then be defined. For instance, t = 0:100. 0 must be the first element of t.
Finally, call Xt = lsode(#dsys, X0, t). After that you should get
Xt(:,1) are the values of h(t)
Xt(:,2) are the values of theta(t)
Xt(:,3) are the values of H(t)=(dh/dt)(t)
Xt(:,4) are the values of J(t)=(dtheta/dt)(t)
So I want to ask whether there's any way to define and solve a system of differential equations in R using matrix notation.
I know usually you do something like
lotka-volterra <- function(t,a,b,c,d,x,y){
dx <- ax + bxy
dy <- dxy - cy
return(list(c(dx,dy)))
}
But I want to do
lotka-volterra <- function(t,M,v,x){
dx <- x * M%*% x + v * x
return(list(dx))
}
where x is a vector of length 2, M is a 2*2 matrix and v is a vector of length 2. I.e. I want to define the system of differential equations using matrix/vector notation.
This is important because my system is significantly more complex, and I don't want to define 11 different differential equations with 100+ parameters rather than 1 differential equation with 1 matrix of interaction parameters and 1 vector of growth parameters.
I can define the function as above, but when it comes to using ode function from deSolve, there is an expectation of parms which should be passed as a named vector of parameters, which of course does not accept non-scalar values.
Is this at all possible in R with deSolve, or another package? If not I'll look into perhaps using MATLAB or Python, though I don't know how it's done in either of those languages either at present.
Many thanks,
H
With my low reputation (points), I apologize for posting this as an answer which supposedly should be just a comment. Going back, have you tried this link? In addition, in an attempt to find an alternative solution to your problem, have you tried MANOPT, a toolbox of MATLAB? It's actually open source just like R. I encountered MANOPT on a paper whose problem boils down to solving a system of ODEs involving purely matrices.
Hello I would like some help on how to use some functions in R.
I have to find the value of a parameter that satisfies my equation. My equation is an integral. So I have to find a way to combine those two functions. The value of a must be less than 5
INTEGRAND<- function(x,a){exp(-x*a)*(1-exp(-sqrt(a)) }
INTEGRAL <- function(a){(integrate(INTEGRAND,lower=0, upper=Inf))$value - 1}
root<- uniroot(INTEGRAL,interval=c(0.01,4.99))
But to calculate the integral we need a value for 'a' but the is is what I am searching for.
I am trying to minimize a quadratic objective with quadratic constraints, is Rolnp the way to go? I have been reading the documentation and it seems like all the examples use equations instead of vector manipulation. All of my parameters are vectors and matrices and they can be quite large. Here is my problem:
X<-([Cf]+[H])%*%[A]
Y<-([Cf]+[H]-[R])%*%[B]
I want to find H that minimizes Y%*%Dmat%*%t(Y) for a given value of X%*%Dmat%*%t(X)
Cf, R, A, Dmat and B are matrices of constants.
The values for H sohould be between 0 and 1.
Is it possible to use Rsolnp to find the vector H even though the input functions will all return other vectors?
I ended up using AUGLAG and COBYLA to solve this problem.
i need to find acceleration of an object the formula for that given in text is a = d^2(L)/d(T)^2 , where L= length and T= time
i calculated this in matlab by using this equation
a = (1/(T3-T1))*(((L3-L2)/(T3-T2))-((L2-L1)/(T2-T1)))
or
a = (v2-v1)/(T2-T1)
but im not getting the right answers ,can any body tell me how to find (a) by any other method in matlab.
This has nothing to do with matlab, you are just trying to numerically differentiate a function twice. Depending on the behaviour of the higher (3rd, 4th) derivatives of the function this will or will not yield reasonable results. You will also have to expect an error of order |T3 - T1|^2 with a formula like the one you are using, assuming L is four times differentiable. Instead of using intervals of different size you may try to use symmetric approximations like
v (x) = (L(x-h) - L(x+h))/ 2h
a (x) = (L(x-h) - 2 L(x) + L(x+h))/ h^2
From what I recall from my numerical math lectures this is better suited for numerical calculation of higher order derivatives. You will still get an error of order
C |h|^2, with C = O( ||d^4 L / dt^4 || )
with ||.|| denoting the supremum norm of a function (that is, the fourth derivative of L needs to be bounded). In case that's true you can use that formula to calculate how small h has to be chosen in order to produce a result you are willing to accept. Note, though, that this is just the theoretical error which is a consequence of an analysis of the Taylor approximation of L, see [1] or [2] -- this is where I got it from a moment ago -- or any other introductory book on numerical mathematics. You may get additional errors depending on the quality of the evaluation of L; also, if |L(x-h) - L(x)| is very small numerical substraction may be ill conditioned.
[1] Knabner, Angermann; Numerik partieller Differentialgleichungen; Springer
[2] http://math.fullerton.edu/mathews/n2003/numericaldiffmod.html