We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.

Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the ...

For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single- and multiple-period settings. We show that the problem of finding the ...

Based on the recent approach of Bertsimas and Sim (2004, 2003) to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives ...

We consider the network loading problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity flow formulation of the problem, we state a decomposition property obtained ...

For the problem of selecting p items with interval objective function coefficients so as to maximize total profit, we introduce the r-restricted robust deviation criterion and seek solutions that minimize the r-restricted ...

The purpose of this note is to give a probability bound on symmetric matrices to improve an error bound in the Approximate S-Lemma used in establishing levels of conservatism results for approximate robust counterparts.

We examine the problem of setting optimal incentives for a portfolio manager hired by an investor who wants to induce ambiguity-robust portfolio choices with respect to estimation errors in expected returns. Adopting a ...

In an economy with a negative exponential utility investor facing a set of risky assets with normally distributed returns over multiple periods, we consider the problem of making an ambiguityrobust dynamic portfolio choice ...

We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. Confidence is here represented using ellipsoidal uncertainty sets for ...