  In many real world problems, optimization decisions have to be made with
limited information. The decision maker may have no a priori or posteriori data
about the often nonconvex objective function except from on a limited number of
points that are obtained over time through costly observations. This paper
presents an optimization framework that takes into account the information
collection (observation), estimation (regression), and optimization
(maximization) aspects in a holistic and structured manner. Explicitly
quantifying the information acquired at each optimization step using the
entropy measure from information theory, the (nonconvex) objective function to
be optimized (maximized) is modeled and estimated by adopting a Bayesian
approach and using Gaussian processes as a state-of-the-art regression method.
The resulting iterative scheme allows the decision maker to solve the problem
by expressing preferences for each aspect quantitatively and concurrently.
