quadprog {modopt.matlab}

MatLab(R)-style Quadratic Programming in R using ROI

Description

quadprog provides a simple interface to ROI using the optimization model specification of MatLab(R)

minimize in x: f'*x + 0.5*x'*H*x subject to: A*x <= b Aeq*x == beq x >= lb x <= ub

Usage

quadprog(H, f, A = NULL, b = NULL, Aeq = NULL, beq = NULL,
  lb = NULL, ub = NULL, x0 = NULL, options = NULL)

Arguments

H

Quadratic term (matrix) of the objective function

f

Linear term (vector) of the objective function

A

Inequality constraints (left-hand side)

b

Inequality constraints (right-hand side)

Aeq

Equality constraints (left-hand side)

beq

Equality constraints (right-hand side)

lb

Lower bound

ub

Upper bound

x0

Initial solution

options

Additional optimization parameters

Value

The solution vector in x as well as the objective value in fval.

Author(s)

Ronald Hochreiter, [e-mail]

Examples

# Covariance matrix of four stocks (weekly returns from 2011):
#
#              AAPL          IBM         MSFT         ORCL
# AAPL 0.0014708114 0.0006940036 0.0006720841 0.0008276391
# IBM  0.0006940036 0.0009643581 0.0006239411 0.0011266429
# MSFT 0.0006720841 0.0006239411 0.0009387707 0.0008728736
# ORCL 0.0008276391 0.0011266429 0.0008728736 0.0021489512

covariance = matrix(c(0.0014708114, 0.0006940036, 0.0006720841, 0.0008276391, 
                      0.0006940036, 0.0009643581, 0.0006239411, 0.0011266429, 
                      0.0006720841, 0.0006239411, 0.0009387707, 0.0008728736, 
                      0.0008276391, 0.0011266429, 0.0008728736, 0.0021489512), 
                      nrow=4, byrow=TRUE)
assets <- dim(covariance)[1]

H <- covariance
f <- rep(0, assets)
Aeq <- rep(1, assets)
beq <- 1
lb <- rep(0, assets)
ub <- rep(1, assets)

solution <- quadprog(H, f, NULL, NULL, Aeq, beq, lb, ub)
portfolio <- solution$x
print(portfolio)