A Universal and Structured Way to Derive Dual Optimization Problem Formulations

References

• Alber M, Nüsslin F (2001) A representation of an NTCP function for local complication mechanisms. Physics Medicine Biol. 46(2):439–447.Google Scholar
• Ben-Israel A, Greville TNE (2003) Generalized Inverses: Theory and Applications, 2nd ed. (Springer, New York).Google Scholar
• Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, Engineering Applications (SIAM, Philadelphia).Google Scholar
• Ben-Tal A, Ben-Israel A, Teboulle M (1991) Certainty equivalents and information measures: duality and extremal principles. J. Math. Anal. Appl. 157(1):211–236.Google Scholar
• Ben-Tal A, den Hertog D, Vial J-P (2015) Deriving robust counterparts of nonlinear uncertain inequalities. Math. Programming 149(1–2):265–299.Google Scholar
• Ben-Tal A, den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Borwein JM, Lewis AS (2000) Convex Analysis and Nonlinear Optimization: Theory and Examples (Springer, New York).Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Google Scholar
• den Hertog D (1994) Interior Point Approach to Linear, Quadratic and Convex Programming (Kluwer, Dordrecht).Google Scholar
• Duffin RJ, Peterson EL, Zener C (1967) Geometric Programming: Theory and Application (Wiley, New York).Google Scholar
• Fiacco AV, McCormick GP (1990) Nonlinear Programming: Sequential Unconstrained Minimization Techniques (SIAM, Philadelphia).Google Scholar
• Gorissen BL, den Hertog D (2015) Robust nonlinear optimization via the dual. Preprint, submitted April 29, http://www.optimization-online.org/DB_HTML/2015/04/4886.html.Google Scholar
• Gushchin AA (2008) On an extension of the concept of f-divergence. Theory Probab. Appl. 52(3):439–455.Google Scholar
• Hiriart-Urruty J-B (2006) A note on the Legendre-Fenchel transform of convex composite functions. Alart P, Maisonneuve O, Rockafellar RT, eds. Nonsmooth Mechanics and Analysis (Springer, New York), 35–46.Google Scholar
• Jansen B, de Jong JJ, Roos C, Terlaky T (1997) Sensitivity analysis in linear programming: Just be careful! Eur. J. Oper. Res. 101(1):15–28.Google Scholar
• Magnanti TL (1974) Fenchel and Lagrange duality are equivalent. Math. Programming 7(1):253–258.Google Scholar
• Niemierko A (1999) A generalized concept of equivalent uniform dose (EUD). Medical Physics 26(6):1100.Google Scholar
• Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
• Romeijn EH, Dempsey JF, Li JG (2004) A unifying framework for multi-criteria fluence map optimization models. Physics Medicine Biol. 49(10):1991–2013.Google Scholar
• Slater ML (2014) Lagrange multipliers revisited. Giorgi G, Kjeldsen TH, eds. Traces and Emergence of Nonlinear Programming (Birkhäuser Verlag, Basel, Switzerland), 293–306.Google Scholar
• Stavreva P, Hristov D, Warkentin B, Fallone B (2003) Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy. Medical Physics 30(5):2948–2958.Google Scholar
• Terlaky T (1985) Onlpprogramming. Eur. J. Oper. Res. 22(1):70–100.Google Scholar
• Tomioka R (2010) Three strategies to derive a dual problem. Preprint, submitted May 8, https://www.scribd.com/document/31522215/Three-strategies-to-derive-a-dual-problem.Google Scholar