Duality in Geometrically Linear Systems
This chapter presents some important mathematical duality theories in geometrically linear, nonconvex and nonsmooth variational problems. By introduction of a so-called indicator functional of the feasible sets, many different problems subject to equality or inequality constraints can be put in a unified framework. The intrinsic relations among these well-known duality theories are revealed and the duality theory in geometrically linear systems is presented in a systematical way. The goal of this chapter is construction not proof. For readers who are seriously interested in the mathematical details of these topics, we refer to the some well-known books by Ekeland and Temam (1976), Zeidler (1988), Ekeland (1990), Aubin (1993) as well as the recent monograph by Motreanu and Panagiotopoulos (1999) for details. However, readers who is not interested in these mathematical details can certainly omit this chapter and continue to the next chapter without difficulty.
KeywordsBanach Space Variational Inequality Complementarity Problem Duality Theory Duality Theorem
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