Book Image

Mastering Scientific Computing with R

Book Image

Mastering Scientific Computing with R

Overview of this book

Table of Contents (17 chapters)
Mastering Scientific Computing with R
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Preface
Index

Quadratic programming


Quadratic programming is an optimization problem where the objective function is quadratic and the constraint functions are linear. We can solve quadratic programs in R using the solve.QP() function part of the quadprog package. Quadratic programs are often expressed in the form of the following equation:

The preceding equation is subject to the following constraints:

However, the solve.QP() function requires that your quadratic program be written in the standard form:

The preceding equation is subject to the following constraint:

In the preceding constraint, T is the mathematical symbol for transpose (matrix A, but with its rows swapped for columns), is a vector of p unknowns, G is a positive definite symmetric matrix, d is a vector of length p, A is a matrix, and b is a vector with the length of the number of constraints c. For example, let's solve the following quadratic program:

The preceding equation is subject to the following constraints:

First, we install the...