To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems. Moreover, an appropriate concept of convergence of filters is developed, and stability of the minimizing filter as well as its approximation by the exterior penalty function technique are proved by using a compactification of the problem.
@article{104393,
author = {Tom\'a\v s Roub\'\i \v cek},
title = {Constrained optimization: A general tolerance approach},
journal = {Applications of Mathematics},
volume = {35},
year = {1990},
pages = {99-128},
zbl = {0714.49006},
mrnumber = {1042847},
language = {en},
url = {http://dml.mathdoc.fr/item/104393}
}
Roubíček, Tomáš. Constrained optimization: A general tolerance approach. Applications of Mathematics, Tome 35 (1990) pp. 99-128. http://gdmltest.u-ga.fr/item/104393/
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