An Algorithm for Quadratic Programming with Applications in Statistics
نویسنده
چکیده
Problems involving estimation and inference under linear inequality constraints arise often in statistical modeling. In this paper we propose an algorithm to solve the quadratic programming problem of minimizing ψ(θ) = θ′Qθ−2c′θ for positive-definite Q, where θ is constrained to be in a closed polyhedral convex cone C = {θ : Aθ ≥ d}, and the m×n matrix A is not necessarily full row-rank. The three-step algorithm is intuitive and easy to code, and the method also provides an algorithm for isotonic regression that is faster than the classic pooled adjacent violators algorithm. Code is provided in the R programming language.
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