Bilevel derivative-free optimization and its application to robust optimization

Optimization Methods and Software

Volumn 27, Issue 3, 2012, Pages 561-577

  Conn, A R ^a   Vicente, L N ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

bilevel programming; derivative free optimization (DFO); quadratic interpolation; robust optimization; simulation based optimization; trust region methods

Indexed keywords

BI-LEVEL PROGRAMMING; DERIVATIVE-FREE OPTIMIZATION; QUADRATIC INTERPOLATION; ROBUST OPTIMIZATION; SIMULATION-BASED OPTIMIZATIONS; TRUST-REGION METHODS;

ALGORITHMS; CORE LEVELS; IMAGE REGISTRATION; INTERPOLATION;

OPTIMIZATION;

EID: 84859789571     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2010.547579     Document Type: Article

References (17)

1. A. Bandeira, K. Scheinberg, and L.N. Vicente, Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization, in preparation (2011).
2. J.F. Bard, Practical Bilevel Optimization: Algorithms and Applications, Kluwer Academic Publishers, Dordrecht, 1998.
3. D. Bertsimas, O. Nohadani, and K.M. Teo, Robust optimization for unconstrained simulation-based problems, Oper. Res. 58 (2010), pp. 161-178.
4. A. Cascon, C. Keating, and W. Shadwick, The Omega function, Tech. Rep., The Finance Development Centre, London, 2002.
5. L.M. Case, An l1 penalty function approach to the nonlinear bilevel programming problem, Ph.D. thesis, University ofWaterloo, Canada, 1997.
6. A.R. Conn, K. Scheinberg, and Ph.L. Toint, On the convergence of derivative-free methods for unconstrained optimization, in Approximation Theory and Optimization, Tributes to M.J.D. Powell, M.D. Buhmann and A. Iserles, eds., Cambridge University Press, Cambridge, 1997, pp. 83-108.
7. A.R. Conn, N.I.M. Gould, and Ph.L. Toint, Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2000.
8. A.R. Conn, K. Scheinberg, and L.N. Vicente, Geometry of interpolation sets in derivative free optimization, Math. Program. 111 (2008), pp. 141-172.
9. A.R. Conn, K. Scheinberg, and L.N.Vicente, Global convergence of general derivative-free trust-region algorithms to first and second order critical points, SIAM J. Optim. 20 (2009), pp. 387-415.
10. A.R. Conn, K. Scheinberg, and L.N. Vicente, Introduction to Derivative-Free Optimization, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2009.
11. S. Dempe, Foundations of Bilevel Programming, Kluwer Academic Publishers, Dordrecht, 2002.
12. G. Fasano, J.L. Morales, and J. Nocedal, On the geometry phase in model-based algorithms for derivative-free optimization, Optim. Methods Softw. 24 (2009), pp. 145-154.
13. S.J. Kane, M.C. Bartholomew-Biggs, M. Cross, and M. Dewar, Optimizing Omega, J. Global Optim. 45 (2009), pp. 153-167.
14. B. Minsky, M. Obradovic, Q. Tang, and R. Thapar, Applying a global optimisation algorithm to fund of hedge funds portfolio optimisation, 2009.
15. J.M. Ortega andW.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, NewYork, 1970.
16. M.J.D. Powell, Least Frobenius norm updating of quadratic models that satisfy interpolation conditions, Math. Program. 100 (2004), pp. 183-215.
17. K. Shimizu, Y. Ishizuka, and J.F. Bard, Nondifferentiable and Two-Level Mathematical Programming, Kluwer Academic Publishers, Boston, 1997.