A Robust Optimization Perspective on Stochastic Programming

Xin Chen · Melvyn Sim · Peng Sun

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Risk and Portfolio Optimization Advanced Optimization Algorithms Research Probabilistic and Robust Engineering Design

Abstract

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a tractable approximation approach for solving a class of multistage chance-constrained stochastic linear optimization problems. An attractive feature of the framework is that we convert the original model into a second-order cone program, which is computationally tractable both in theory and in practice. We demonstrate the framework through an application of a project management problem with uncertain activity completion time.

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References

2011Introduction to Stochastic Programming 2004The Price of Robustness 1959Chance-Constrained Programming 1998Robust Convex Optimization 1999Robust solutions of uncertain linear programs 2000Robust solutions of Linear Programming problems contaminated with uncertain data 1995Stochastic Programming 2004Adjustable robust solutions of uncertain linear programs

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2018Adaptive Distributionally Robust Optimization 2009From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization 2011A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization 2009Primal and dual linear decision rules in stochastic and robust optimization 2007A Linear Decision-Based Approximation Approach to Stochastic Programming 2017Data-driven robust optimization based on kernel learning

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