Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization

References

• Ben-Tal A, Nemirovski A (2001) On polyhedral approximations of the second-order cone. Math. Oper. Res. 26(2):193–205.Link, Google Scholar
• Bertsimas D, de Ruiter F (2016) Duality in two-stage adaptive linear optimization: Faster computation and stronger bounds. INFORMS J. Comput. 28(3):500–511.Link, Google Scholar
• Birge J, Louveaux F (2011) Introduction to Stochastic Programming (Springer Science & Business Media, New York).Crossref, Google Scholar
• Boni O, Ben-Tal A (2008) Adjustable robust counterpart of conic quadratic problems. Math. Methods Oper. Res. 68(2):211–233.Crossref, Google Scholar
• Hadjiyiannis M, Goulart P, Kuhn D (2011) A scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization. Proc. IEEE Conf. Decision Control Eur. Control Conf. (CDC-ECC, Orlando, FL), 7386–7391.Google Scholar
• Hanasusanto G, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls. Oper. Res. 66(3):849–869. Link, Google Scholar
• Pinar M, Tütüncü R (2005) Robust profit opportunities in risky financial portfolios. Oper. Res. Lett. 33(4):331–340.Crossref, Google Scholar
• Rockafellar R (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Roos E, den Hertog D, Ben-Tal A, de Ruiter F, Zhen J (2018) Tractable approximation of hard uncertain optimization problems. Preprint, submitted June 27, http://www.optimization-online.org/DB_HTML/2018/06/6679.html.Google Scholar
• Takeda A, Taguchi S, Tütüncü R (2008) Adjustable robust optimization models for a nonlinear two-period system. J. Optim. Theory Appl. 136(2):275–295.Crossref, Google Scholar
• Xu G, Burer S (2018) A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides. Comput. Optim. Appl. 70(1):33–59.Crossref, Google Scholar
• Zeng B, Zhao L (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5):457–461.Crossref, Google Scholar
• Zhen J, den Hertog D, Sim M (2017) Adjustable robust optimization via Fourier-Motzkin elimination. Oper. Res. 66(4):1086–1100.Link, Google Scholar