I consider an application a "true" one if it does not come as a reformulation of an optimization problem. I already know about applications of the second order and positive semidefinite cone-complementarity problems which are reformulations of optimization problems (for example related to Nash equilibrium). I also know about true practical applications where the cone is either the nonnegative orthant or the direct product of the nonnegative orthant with a Euclidean space. However I don't consider the later cones essentially different from the nonnegative orthant. I am mostly interested in practical applications, but I am also interested in possible applications of cone-complementarity to another field of mathematics. I would be grateful if you could point me to any papers, books, links or other materials in this topic.
Dear Sandor
I think there is a nice application in applied mechanics, where friction and impacts are formulated as a complementarity problem. Please have a look at a book on Multibody Dynamics with Unilateral Contacts by Friedrich Pfeiffer and Christoph Glocke.
Best wishes
Marian.
Thank you very much. I am eager to see the application, because all applications in mechanics related to friction which I have seen are related to nonnegativity of parameters and in this way they are complementarity problems on the nonnegative orthant. I will come back to you with a more informed answer.
Dear Marian
I checked the book, but it seems that all applications are for the nonnegative orthant. I know about applications of second order cone complementarity problems (SOCCP) in elastoplasticity and economics.
For example:
Zhang, L. L.; Li, J. Y.; Zhang, H. W.; Pan, S. H.
A second order cone complementarity approach for the numerical solution of elastoplasticity problems. Comput. Mech. 51 (2013), no. 1, 1–18.
However, in all applications which I know (including the above one) the SOCCP occur as reformulation of an optimization problem.
You can find applications in the References list of the paper below. However, all this applications come from reformulations of conic optimization problems. So the new question is: Are there any applications which do not come from optimization?
Preprint Conic optimization and complementarity problems
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