Abstract We introduce a new sequential algorithm for the Standard Quadratic Programming Problem (StQP), which exploits a formulation of StQP as a Linear Program with Linear Complementarity Constraints (LPLCC). The algorithm is finite and guarantees at least in theory a $$\delta $$ δ -approximate global minimum for an arbitrary small $$\delta $$ δ , which is a global minimum in practice. The sequential algorithm has two phases. In Phase 1, Stationary Points (SP) with strictly decreasing objective function values are computed. Phase 2 is designed for giving a certificate of global optimality for the last SP computed in Phase 1. Two different Nonlinear Programming Formulations for LPLCC are proposed for each one of these phases, which are solved by efficient enumerative algorithms. New procedures for computing a lower bound for StQP are also proposed, which are easy to implement and give tight bounds in general. Computational experiments with a number of test problems from known sources indicate that the two-phase sequential algorithm is, in general, efficient in practice. Furthermore, the algorithm seems to be an efficient way to study the copositivity of a matrix by exploiting an StQP with this matrix.

Recently, it has been shown that complementarity models are an attracting tool for representing power converters in both open- and closed-loop configuration. A unique dynamical complementarity model captures all the modes of a power converter, without assuming the a priori knowledge of the sequence of modes or of the switching time instants. In this paper, we derive the complementarity model of a single-phase active filter with cascaded multilevel inverter. A combination of the unipolar and the phase-disposition PWM techniques is used with the goal of regulating the dc-link voltage. As benchmark for comparison, the time evolution of inductors currents and capacitors voltages computed with the complementarity procedure is compared with the ones obtained with PSIM software.