New a priori and a posteriori probabilistic bounds for robust counterpart optimization: III. Exact and near-exact a posteriori expressions for known probability distributions

摘要: Abstract The performance of robust optimization is closely connected with probabilistic bounds that determine the probability constraint violation due to uncertain parameter realizations. In Part I this work, new a priori and posteriori were developed for cases when applied problems parameters whose distributions unknown. II, focus shifted known bounds. paper, new, tight expressions are constraints containing specific distributions, is, those attributed normal, uniform, discrete, gamma, chi-squared, Erlang, or exponential distributions. nature some requires efficient implementations, algorithmic methods discussed which greatly improve applicability. These much tighter than existing reduce conservatism solutions. theoretical results Parts I, III allow wider usage in process synthesis operations research applications.