We develop the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. A robust decision-making framework is built on a utility set which characterizes a decision maker’s risk attitude described by boundary and auxiliary conditions. This framework is studied using the Sample Average Approximation (SAA) approach. We show the … Read more
We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in \cite{KlaKum02}. In particular, we show that constraint nondegeneracy and hence uniqueness of the multiplier is necessary for the Aubin property of the critical point map. Moreover, we give conditions under which the critical point … Read more
Chance constrained programming is an effective and convenient approach to control risk in decision making under uncertainty. However, due to unknown probability distributions of random parameters, the solution obtained from a chance constrained optimization problem can be biased. In practice, instead of knowing the true distribution of a random parameter, only a series of historical … Read more
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2010, pp. 219–229], … Read more
In 2001, info-gap decision theory re-invented the then 40-year old model of local robustness, known universally as radius of stability (circa 1960). Since then, this model of local robustness has been promoted by info-gap scholars as a reliable tool for the management of a severe uncertainty that is characterized by a vast (e.g. unbounded) uncertainty … Read more
This note suggests the implicit function theorem for generalized equations, unifying Robinson’s theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings. Article Download View STRONGLY REGULAR NONSMOOTH GENERALIZED EQUATIONS (REVISED)
In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more