METHOD FOR SOLVING CONVEX QUADRATIC PROGRAM FOR CONVEX SET

摘要

A method solves a convex quadratic program (QP) for a convex set. Constrains of the QP include sets of linear equalities and linear inequalities. The solving uses an Alternating Direction Method of Multipliers (ADMM). Variables of the convex QP include a linear subspace constrained variable vector and a set constrained variable vector. The method solves the linear subspace constrained variable vector while keeping the set constrained variable vector fixed using an optimal step size and a Lagrangian multiplier, and solves the set of constrained variable vector while keeping linear subspace constrained variable vector fixed using the optimal step size and the Lagrangian multiplier. Then, the Lagrangian multiplier is updated. A feasible solution is outputted if a termination condition for the feasible solution is satisfied, and an infeasible solution is signaled if a termination condition for the satisfied for the infeasible solution is satisfied. Otherwise, the steps are repeated.