It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical meanvariance theory. The first model is an extension of the tradition...

This paper contemplates the use of robust optimization as a framework for addressing problems that involve endogenous uncertainty, i.e., uncertainty that is affected by the decision maker’s strategy. To that end, we extend generic polyhedral uncertainty sets typically considered in robust optimization into sets that depend on the actual decisions. We present the derivation of robust counterpart...

We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart proble...

This paper considers an underlay access strategy for coexisting wireless networks where the secondary system utilizes the spectrum owned by the primary system to simultaneously support multiple secondary users. In the considered scenario, the throughput performance of each system is limited by the interference imposed by the other. Hence, improving the performance of one system conflicts with t...

In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is permitted to modify the initial decision. We treat the uncertainty using the framework of robust optimization in which uncertain parameters lie within a given ...

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii) binary decisions and iii) hard constraints within an ellipsoidal uncertainty set, this paper provides a different interpretation of their robust counterpart (R...

A novel data-driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M-estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over-conservatism. Robust kernel density estimation with Hampel loss function is employed ...

Robust optimization considers optimization problems with uncertainty in the data. The common data model assumes that the uncertainty can be represented by an uncertainty set. Classic robust optimization considers the solution under the worst case scenario. The resulting solutions are often too conservative, e.g., they have high costs compared to non-robust solutions. This is a reason for the de...

This document provides a brief proposal for “Robust Optimization & Robust Control Synthesis” reading group.