This book examines optimization problems that in practice involve random model parameters. It
details the computation of robust optimal solutions i.e. optimal solutions that are
insensitive with respect to random parameter variations where appropriate deterministic
substitute problems are needed. Based on the probability distribution of the random data and
using decision theoretical concepts optimization problems under stochastic uncertainty are
converted into appropriate deterministic substitute problems. Due to the probabilities and
expectations involved the book also shows how to apply approximative solution techniques.
Several deterministic and stochastic approximation methods are provided: Taylor expansion
methods regression and response surface methods (RSM) probability inequalities multiple
linearization of survival failure domains discretization methods convex approximation
deterministic descent directions efficient points stochastic approximation and gradient
procedures and differentiation formulas for probabilities and expectations. In the third
edition this book further develops stochastic optimization methods. In particular it now
shows how to apply stochastic optimization methods to the approximate solution of important
concrete problems arising in engineering economics and operations research.
