MAFS6010R- Portfolio Optimization with R
MSc in Financial Mathematics
Fall 2018-19, HKUST, Hong Kong

This R session will introduce different solvers in R that can be used for portfolio optimization.

For an overwhelming amount of information on the many solvers for R, see the Task View on Optimization and Mathematical Programming.

John Nash, the author of many of the optimization packages (not to be confused with the main character of the movie *A Beautiful Mind*), has an interesting and insightful blog: https://nashjc.wordpress.com. In particular, the entry on choosing which method to use for “optimizing” functions is recommended as a guide on how to navigate the overwhelming amount of solvers in R.

General solvers can deal with arbitrary nonlinear optimization problems, at the expense of perhaps slow convergence and risk of numerical issues.

Package **stats** (base R package installed by default) offers several general purpose optimization routines.

`optimize()`

: For one-dimensional unconstrained function optimization over an interval (for one-dimensional root finding use`uniroot()`

).

```
f <- function(x) exp(-0.5*x) * sin(10*pi*x)
f(0.5)
#> [1] 4.768779e-16
result <- optimize(f, interval = c(0, 1), tol = 0.0001)
result
#> $minimum
#> [1] 0.3494978
#>
#> $objective
#> [1] -0.8395633
str(result)
#> List of 2
#> $ minimum : num 0.349
#> $ objective: num -0.84
# let's plot something
curve(f, 0, 1, n = 200, col=4); grid()
points(result$minimum, result$objective, pch = 20, col = "red", cex = 1.5)
```