Explicit Surrogate Dual Formulation and Algorithm for Quadratic Programming

Abstract

There are some characteristics in the surrogate dual for mathematical programming, such as the quasi concavity of the objective function of the dual problem, the surrogate multipliers in the simplex, i.e. $\sum\nolimits_{i = 1}^m {\lambda _i } = 1$ , which give much convenient conditions for constructing algorithms for solving the surrogate dual problem. In the theory of surrogate dual, the objective function is expressed only in implicit form, which may bring difficulties to the numerical treatment. In this paper a novel approach on the explicit form of surrogate dual problem, quasi active set and interior point algorithm is presented to solve quadratic programming problem, and some quadratic programming problems are constructed to verify the approach.