  A framework is proposed for solving general convex quadratic programs (CQPs)
from an infeasible starting point by invoking an existing feasible-start
algorithm tailored for inequality-constrained CQPs. The central tool is an
exact penalty function scheme equipped with a penalty-parameter updating rule.
The feasible-start algorithm merely has to satisfy certain general
requirements, and so is the updating rule. Under mild assumptions, the
framework is proved to converge on CQPs with both inequality and equality
constraints and, at a negligible additional cost per iteration, produces an
infeasibility certificate, together with a feasible point for an
(approximately) $\ell_1$-least relaxed feasible problem when the given problem
does not have a feasible solution. The framework is applied to a feasible-start
constraint-reduced interior-point algorithm previously proved to be highly
performant on problems with many more constraints than variables
("imbalanced"). Numerical comparison with popular codes (SDPT3, SeDuMi, MOSEK)
is reported on both randomly generated problems and support-vector machine
classifier training problems. The results show that the former typically
outperforms the latter on imbalanced problems.
