In this paper we present a robust conjugate duality theory for convex programming problems in the face of data uncertainty within the framework of robust optimization, extending the powerful conjugate duality technique. We first establish robust strong duality between an uncertain primal parameterized convex programming model problem and its uncertain conjugate dual by proving strong duality be...

This thesis is about robust optimization, a class of mathematical optimization problems which arise frequently in engineering applications, where unknown process parameters and unpredictable external influences are present. Especially, if the uncertainty enters via a nonlinear differential equation, the associated robust counterpart problems are challenging to solve. The aim of this thesis is t...

We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets ...

An optimal planning of future wireless networks is fundamental to satisfy rising traffic demands jointly with the utilization of sophisticated techniques, such as OFDMA. Current methods for this task require a static model of the problem. However, uncertainty of data arises frequently in wireless networks, e. g., fluctuating bit rate requirements. In this paper, robust optimization is applied t...

Robust PCA methods are typically based on batch optimization and have to load all the samples into memory during optimization. This prevents them from efficiently processing big data. In this paper, we develop an Online Robust PCA (OR-PCA) that processes one sample per time instance and hence its memory cost is independent of the number of samples, significantly enhancing the computation and st...

This paper studies the robust optimization for the single allocation p-hub median problem under discount factor uncertainty. We develop the discount factor as a novel uncertain parameter, which represents different connection modes between hubs. The discount factor can be described by a random variable with discrete distribution in nominal case. We apply a robust optimization approach to deal w...

Robust optimization is an approach for optimization under uncertainty that has recently attracted attention both from theory and practitioners. While there is an elaborate and powerful machinery for continuous robust optimization problems, results on robust combinatorial optimization and robust linear integer programs are still rare and hardly general. In a seminal paper Bertsimas and Sim [7] s...

This paper considers evacuation via surface transportation networks in an uncertain environment. We focus on demand uncertainty which can lead to significant infeasibility cost during evacuation, where loss of life or property may appear. We develop a robust linear programming model based on a robust optimization approach where hard constraints are guaranteed within an appropriate uncertainty s...

In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a ...