Translating code that carries out SOCP/SDP optimisation from MATLAB to R - r

Question

I have the following MATLAB code which was used in the linked paper (http://www.optimization-online.org/DB_FILE/2014/05/4366.pdf), and would like to be able to use the Rsocp package to be able to carry out the same function but in R. The Rsocp package is available by using the command:
install.packages("Rsocp", repos="http://R-Forge.R-project.org")
and through the socp() function it carries out a similar function to solvesdp(constraints, -wcvar, ops) in the MATLAB code below.
I do not have MATLAB which makes this problem more difficult for me to solve.
The issue I have is the R's socp() function takes matrices as inputs that reflect the data(/covariance matrix and average return values) and constraints all together, where as the MATLAB code seems to be optimising a function...in this specific case it looks like its optimising -wcvar to get the optimal weights, so I am unsure of how to set up my problem in R to get similar results.
The MATLAB code I would therefore like help in translating to R is as follows:
function [w] = rgop(T, mu, sigma, epsilon)
% This function determines the robust growth-optimal portfolio
% Input parameters:
% T - the number of time periods
% mu - the mean vector of asset returns
% sigma - the covariance matrix of asset returns
% epsilon - violation probability
% Output parameters:
% w - robust growth-optimal portfolios
% the number of assets
n = length(mu);
% portfolio weights
w = sdpvar(n,1);
% mean and standard deviation of portfolio
rp = w'*mu;
sigmap = sqrt(w'*sigma*w);
% preclude short selling
constraints = [w >= 0]; %#ok<NBRAK>
% budget constraint
constraints = [constraints, sum(w) == 1];
% worst-case value-at-risk (theorem 4.1)
wcvar = 1/2*(1 - (1 - rp + sqrt((1-epsilon)/epsilon/T)*sigmap)^2 - ((T-1)/epsilon/T)*sigmap^2);
% maximise WCVAR
ops = sdpsettings('solver','sdpt3','verbose',0);
solvesdp(constraints, -wcvar, ops);
w = double(w);
end
For the square root function of the covariance matrix one can use:
Rsocp:::.SqrtMatrix()
Note this question is partially related to my previous question however is more focused on getting the worst case VaR weights:
SOCP Solver Error for fPortoflio using solveRsocp
Perhaps a good start would be to use this code where the Rsocp package has already been used...
https://r-forge.r-project.org/scm/viewvc.php/pkg/fPortfolio/R/solveRsocp.R?view=markup&root=rmetrics&pathrev=3507
EDIT
I think the MATLAB code for the solvesdp function is available from this link:
https://code.google.com/p/vroster/source/browse/trunk/matlab/yalmip/solvesdp.m?r=11
Also a quick question about SOCP optimisations in general...would the result obtained via SOCP optimisation be the same as that achieved using other methods of optimisation? will the only difference be speed and efficiency?
EDIT2
Since it was requested...
rgop <- function(tp, mu, sigma, epsilon){
# INPUTS
# tp - the number of time periods
# mu - the mean vector of asset returns
# sigma - the covariance matrix of asset returns
# epsilon - violation probability
# OUTPUT
# w - robust growth-optimal portfolios
#n is number of assets
n <- length(mu)
# portfolio weights (BUT THIS IS THE OUTPUT)
# for now will assume equal weight
w <- rep(1/n,n)
# mean and standard deviation of portfolio
rp <- sum(w*mu)
sigmap <- as.numeric(sqrt(t(w) %*% sigma %*% w))
# worst-case value-at-risk (theorem 4.1)
wcvar = 1/2*(1 - (1 - rp + sqrt((1-epsilon)/epsilon/tp)*sigmap)^2 - ((tp-1)/epsilon/tp)*sigmap^2);
# optimise...not sure how to carry out this optimisation...
# which is the main thrust of this question...
# could use DEoptim...but would like to understand the SOCP method
}

Answer 1

SOCP is just a fast way of finding the minimum in cases where you know enough about the problem to constrain it in certain technical ways. As you're discovering these constraints can be tricky to formulate, so it is worth asking if you need the speed. Often the answer is yes, but for debugging/exploration purposes brute numerical optimisation using R's optim function can be fruitful.