Hybrid Algorithms with Index Addition and Subtraction Strategies for Solving Mathematical Programs with Complementarity Constraints

Recently, the authors have presented a hybrid approach for solving mathematical programs with complementarity constraints. This approach employs an active-set identification function and possesses a finite termination property under some appropriate conditions including the so-called asymptotically weak nondegeneracy. In this paper, we continue this work and propose two modified methods, one of which makes use of an index addition strategy and the other utilizes the converse strategy. Both the methods do not require the above-mentioned assumption and also have a finite termination property under very weak assumptions. Numerical experience shows that the proposed approaches are effective.