ИСТИНА

In the context of mixed complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in related theoretical and algorithmic developments. In this presentation, we provide the complete picture of relations between the most important regularity conditions for mixed complementarity problems. We not only summarize the existing results on the subject, but also establish some new relations filling all the gaps in the current understanding of how different types of regularity relate to each other. The regularity conditions to be considered include BD and CD-regularities of the natural residual and Fischer-Burmeister reformulations, strong regularity, and semistablility. A special attention is paid to the particular cases of a nonlinear complementarity problem and of a Karush-Kuhn-Tucker system.