Summary: 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 \(\psi (\theta)=\theta^{\prime}\mathcal Q\theta -2c^{\prime}\theta\) for positive definite Q, where \(\theta\) is constrained to be in a closed polyhedral convex cone \(\mathcal C =\{\theta :A\theta \geq d\}\), and the \(m \times n\) matrix \(A\) is not necessarily full row rank. The three-step algorithm is intuitive and easy to code. Code is provided in the R programming language.