--- title: "Infeasible Primal-Dual Quadratic Programming with Box Constraints" author: "Jan de Leeuw" date: "Version 08, May 09, 2017" output: html_document: keep_md: yes number_sections: yes toc: yes pdf_document: keep_tex: yes number_sections: yes toc: yes toc_depth: 3 fontsize: 12pt graphics: yes bibliography: boxqp.bib abstract: This describes a C version of a infeasible primal-dual algorithm for positive definite quadratic programming with box constraints, proposed by Voglis and Lagaris. We also give a straightforward .C() interface for R. --- {r function_code, echo = FALSE} source("boxqp.R")  {r packages, echo = FALSE} options (digits = 10) library (captioner) mprint <- function (x, d = 6, w = 8, f = "") { print (noquote (formatC ( x, di = d, wi = w, fo = "f", flag = f ))) }  {r equation_numbering, echo = FALSE} figure_nums <- captioner (prefix = "Figure") theorem_nums <- captioner (prefix = "Theorem") lemma_nums <- captioner (prefix = "Lemma") corollary_nums <- captioner (prefix = "Corollary")  Note: This is a working paper which will be expanded/updated frequently. All suggestions for improvement are welcome. The directory [gifi.stat.ucla.edu/boxqp](http://gifi.stat.ucla.edu/boxqp) has a pdf version, the complete Rmd file with all code chunks, the R and C code, and the bib file. #Introduction The problem we address in this paper is minimization of $$\label{E:f} f(x)=\frac12 x'Cx+d'x$$ over $a\leq x\leq b$ (elementwise). Here $C$ is positive definite, so $f$ is strictly convex. Also we assume without loss of generality that \$ab_i\text{ or }(x_i^{(k)}=b_i\text{ and }\mu_i^{(k)}\geq 0)\}\\ S^{(k)}&=\{i\mid a_i