A Simple New Algorithm for Quadratic Programming with Applications in Statistics

Abstract

Problems involving estimation and inference under linear inequality constraints arise often in statistical modeling. In this article, we propose an algorithm to solve the quadratic programming problem of minimizing for positive definite Q, where is constrained to be in a closed polyhedral convex cone , and the m × n matrix is not necessarily full row rank. The three-step algorithm is intuitive and easy to code. Code is provided in the R programming language.

Keywords:

• Cone projection
• Constrained parameter estimation
• Dual algorithm
• Inequality constraints
• Polar cone
• Primal-dual methods
• Restricted least squares
• Shape-restricted regression

Mathematics Subject Classification:

• Primary 65K05
• Secondary 62G05

Acknowledgment

This work was partially supported by NSF DMS 0905656.