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Nonsmooth Approach to Optimization Problems with Equilibrium Constraints - Theory, Applications and Numerical Results (Hardcover, 1998 ed.)
Loot Price: R4,519
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Nonsmooth Approach to Optimization Problems with Equilibrium Constraints - Theory, Applications and Numerical Results (Hardcover, 1998 ed.)
Series: Nonconvex Optimization and Its Applications, 28
Expected to ship within 10 - 15 working days
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In the early fifties, applied mathematicians, engineers and
economists started to pay c10se attention to the optimization
problems in which another (lower-Ievel) optimization problem arises
as a side constraint. One of the motivating factors was the concept
of the Stackelberg solution in game theory, together with its
economic applications. Other problems have been encountered in the
seventies in natural sciences and engineering. Many of them are of
practical importance and have been extensively studied, mainly from
the theoretical point of view. Later, applications to mechanics and
network design have lead to an extension of the problem
formulation: Constraints in form of variation al inequalities and
complementarity problems were also admitted. The term "generalized
bi level programming problems" was used at first but later,
probably in Harker and Pang, 1988, a different terminology was
introduced: Mathematical programs with equilibrium constraints, or
simply, MPECs. In this book we adhere to MPEC terminology. A large
number of papers deals with MPECs but, to our knowledge, there is
only one monograph (Luo et al. , 1997). This monograph concentrates
on optimality conditions and numerical methods. Our book is
oriented similarly, but we focus on those MPECs which can be
treated by the implicit programming approach: the equilibrium
constraint locally defines a certain implicit function and allows
to convert the problem into a mathematical program with a nonsmooth
objective.
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