Deriving robust counterparts of nonlinear uncertain inequalities

Mathematical Programming

Volumn 149, Issue 1-2, 2015, Pages 265-299

  Ben Tal, Aharon ^a,b   den Hertog, Dick ^b   Vial, Jean Philippe ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TILBURG UNIVERSITY   (Netherlands)

^c ORDECSYS Company   (Switzerland)

Author keywords

Fenchel duality; Nonlinear inequality; Robust counterpart; Robust optimization; Support functions

Indexed keywords

NONLINEAR PROGRAMMING;

FENCHEL DUALITY; NONLINEAR INEQUALITY; ROBUST COUNTERPART; ROBUST OPTIMIZATION; SUPPORT FUNCTIONS;

UNCERTAINTY ANALYSIS;

EID: 84921701000     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-014-0750-8     Document Type: Article

References (19)

1. AIMMS: Paragon Decision Technology. http://www.aimms.com/operations-research/mathematical-programming/robust-optimization (2012)
2. Anderson, T.W., Darling, D.A.: Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes. Ann. Math. Stat. 23(2), 193–212 (1952)
3. Averbakh, I., Zhao, Y.-B.: Explicit reformulations for robust optimization problems with general uncertainty sets. SIAM J. Optim. 18(4), 1436–1466 (2007)
4. Ben-Tal, A., Ben-Israel, A., Teboulle, M.: Certainty equivalents and information measures: duality and extremal principles. J. Math. Anal. Appl. 157, 211–236 (1991)
5. Ben-Tal, A., El-Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics (2009)
6. Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization—Analysis, Algorithms, and Engineering Applications. MPS-SIAM Series on Optimization (2001)
7. Ben-Tal, A., den Hertog, D.: Immunizing conic quadratic optimization problems against implementation errors. CentER Discussion Paper 2011–060, Tilburg University, 2011 (to appear in Mathematical Programming)
8. Ben-Tal, A., den Hertog, D., De Waegenaere, A.M.B., Melenberg, B., Rennen, G.: Robust solutions of optimization problems affected by uncertain probabilities. Manag. Sci. 59(2), 341–357 (2013)
9. Ben-Tal, A., den Hertog, D., Laurent, M.: Hidden Convexity in Partially Separable Optimization. CentER Discussion Paper 2011-070, Tilburg University (2011)
10. Bertsimas, D., Brown, D., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)
11. Bertsimas, D., Pachamanova, D., Sim, M.: Robust linear optimization under general norms. Oper. Res. Lett. 32, 510–516 (2004)
12. den Hertog, D.: Interior Point Approach to Linear, Quadratic and Convex Programming. Kluwer, Dordrecht (1994)
13. Goh, J., Sim, M.: Robust optimization made easy with ROME. Oper. Res. 59(4), 973–985 (2011)
14. Golub, G.H., van Loan, C.F.: Matrix Computations, 2nd edn. Johns Hopkins University Press, London (1989)
15. Gushchin, A.A.: On an extension of the notion of $$f$$f-divergence. Theory Probab. Its Appl. 52(3), 439–455 (2008)
16. Löfberg, J.: Automatic robust convex programming. Optim. Methods Softw. 27(1), 115–129 (2012)
17. Nemirovski, A.: Lectures on Robust Convex Optimization. Lecture 2 of Lecture Notes. http://www2.isye.gatech.edu/nemirovs/Lect2 (2009)
18. Nesterov, Y.E., Nemirovski, A.: Interior Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied Mathematics, Philadelphia (1993)
19. Rockafellar, R.T.: Convex Analysis. Princeton Press, Princeton (1970)