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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/540 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/540 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/540 archive 351 disk0/00/00/05/24 2016-01-15 01:43:08 2021-08-27 17:08:16 2016-01-15 01:43:08 monograph show 2 Mifflin R. AL0268 pub iis_met prog_sds We introduce semismooth and semiconvex functions and discuss their properties with respect to nonsmooth nonconvex constrained optimization problems. These functions are locally Lipschitz, and hence have generalized gradients. The author has given an optimization algorithm that uses generalized gradients of the problem functions and converges to stationary points if the functions are semismooth. If the functions are semiconvex and a constraint qualification is satisfied, then we show that a stationary point is an optimal point. We show that the pointwise maximum or minimum over a compact family of continuously differentiable functions is a semismooth function and that the pointwise maximum over a compact family of semiconvex functions is a semiconvex function. Furthermore, we show that a semismooth composition of semismooth functions is semismooth and gives a type of chain rule for generalized gradients. 1976-12 published RR-76-021 RR-76-021 2190 public research_report IIASA, Laxenburg, Austria 23 TRUE FALSE info:eu-repo/semantics/book