Contributed Session Wed.1.MA 313

Wednesday, 10:30 - 12:00 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Advances in the theory of complementarity and related problems I


Chair: Jein-Shan Chen



Wednesday, 10:30 - 10:55 h, Room: MA 313, Talk 1

Jein-Shan Chen
Lipschitz continuity of solution mapping of symmetric cone complementarity problem

Coauthor: Xinhe Miao


This paper investigates the Lipschitz continuity of the solution mapping
of symmetric cone (linear or nonlinear) complementarity problems (SCLCP
or SCCP, respectively) over Euclidean Jordan algebras. We show that if
the transformation has uniform Cartesian P-property, then the solution
mapping of the SCCP is Lipschitz continuous. Moreover, we establish that
the monotonicity of mapping and the Lipschitz continuity of solutions of
the SCLCP imply ultra P-property, which is a concept recently developed
for linear transformations on Euclidean Jordan algebra. For a Lyapunov
transformation, we prove that the strong monotonicity property, the ultra
P-property, the Cartesian P-property and the Lipschitz continuity of
the solutions are all equivalent to each other.



Wednesday, 11:00 - 11:25 h, Room: MA 313, Talk 2

Alexey Svyatoslavovich Kurennoy
On regularity conditions for complementarity problems

Coauthor: Alexey F. Izmailov


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.


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