An interior–exterior approach for convex quadratic programming

In the last decade, a new class of interior–exterior algorithms for linear programming was developed. The method was based on the use of mixed penalty function with two separate parameters to solve a set of sub-penalized problems associated to the initial problem.To study the necessary optimality conditions, one introduced a new concept of the so-called pseudo-gap to describe fully the optimal primal and dual solutions. Only one Newton iteration is sufficient to approximate the solution of penalized problem which satisfies a criterion of proximity.The purpose of this work is to extend the approach to the convex quadratic programming problems.