  In this paper, based on a $Q$-linear convergence analysis and an estimate of
the linear convergence factor of the proximal point (PP) algorithm for solving
box constrained quadratic programming (BQP) problems, an accelerated proximal
point (APP) algorithm for solving BQP problems is presented. To solve the
strictly convex BQP problems in each step of the APP algorithm, an efficient
homotopy method, which tracks the solution path of a parametric quadratic
program, is given. The algorithm with APP algorithm as outer iteration and the
homotopy method as inner iteration is named by APP-Hom. The inner homotopy
method is efficient by implementing, a warm-start technique based on the
accelerated proximal gradient (APG) method, an $\varepsilon$-relaxation
technique for checking prime and dual feasibility and determining/correcting
the active set. Numerical tests for randomly generated dense and sparse BQPs,
BQPs arising from image deblurring, BQPs in SVM, as well as discretized
obstacle problem, elastic-plastic torsion problem, and the journal bearing
problem show that the APP algorithm takes much less steps than the PP
algorithm, the homotopy method is very efficient for strictly-convex BQP, and
in consequence, that the APP-Hom is very efficient for non-convex BQP.
