DC programming and DCA for globally solving the value-at-risk

Computational Management Science

Volumn 6, Issue 4, 2009, Pages 477-501

  Pham Dinh, Tao ^a   Nam, Nguyen Canh ^a   Le Thi, Hoai An ^b  

^a UNIVERSITÉ ET INSA DE ROUEN   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Bilevel linear programming; Branch and bound; DC programming; DCA; Value at risk

Indexed keywords

EID: 69249203577     PISSN: 1619697X     EISSN: 16196988     Source Type: Journal    
DOI: 10.1007/s10287-009-0099-2     Document Type: Article

References (23)

1. Andersson F, Mausser H, Rosen D, Uryasev S (2001) Credit risk optimization with conditional value-at-risk criterion. Math Programm Ser B 89: 273-291
2. Gilli M, Kellezi A (2002) A global optimization heuristic for portfolio choice with VaR and expected shortfall. In: Kontoghiorghes EJ, Rustem B, Siokos S (eds) Computational Methods in Decision-making, Economics and Finance. Applied Optimization Series. Kluwer Academic Publishers, Dordrecht, pp 167-183
3. Hiriart-Urruty JB, Lemarechal C (1991) Convex analysis and minimization algorithms. Parts I&II. Springer, Heidelberg
4. Le Thi HA, Pham Dinh T (1997) Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. J Glob Optim 11:253-285
5. Le Thi HA, Pham Dinh T, Muu LD (1999) Exact penalty in DC programming. Vietnam J Math 27(2):169-178
6. Hoang T (1995) DC optimization: Theory, methods and algorithms. In: Horst R, Pardalos PM(eds) Handbook of global optimization. Kluwer, Dordecht
7. Hoang T (1998) Convex analysis and global optimization. Kluwer, Dordrecht
8. Horst R, Van Thoai N (1999) DC programming: Overview. J Optim Theory Appl 103:1-43
9. Horst R, Pardalos PM, Van Thoai N (1996) Global optimization: deterministic approaches. Kluwer, Dordrecht
10. Le Thi HA, Pham Dinh T (2002) DC Programming: Theory, algorithms and applications. The State of the Art. A. (ed) The first international workshop on global constrained optimization and constraint satisbfaction (Cocos' 02), Valbonne-Sophia Antipolis, France, October 2-4, 28 pp
11. Le Thi HA, Pham Dinh T (2003) Large scale molecular optimization from distances matrices by a DC optimization approach. SIAM J Optim 14(1):77-116
12. Le Thi HA, Pham Dinh T (2004) DC programming approaches and DCA for globally solving linear complematarity problems. Research report. National Institute for Applied Sciences, Rouen (submitted)
13. Le Thi HA, Pham Dinh T (2005) The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problem. Ann Oper Res 133:23-46
14. Le Thi HA, Pham Dinh T, Ngai HV (2005) Exact penalty techniques in DC programming, Research Report. National Institute for Applied Sciences, Rouen, 38 p
15. Larsen N, Mausser H, Uryasev S (2002) Algorithms for optimization of value-at-risk. In: Pardalos P, Tsitsiringos VK(eds) Financial engineering, E-commerce and supply chain. Kluwer, Norwell, pp 129-157
16. Luo Z-Q, Pang J-S, Ralph D, Wu S-Q (1996) Exact penalization and stationary conditions of mathematical programs with equilibrium constraints. Math Programm 75:19-76
17. Pang J-S, Leyffer S (2004) On the global minimization of the value-at-risk. Optim Methods Softw 19(5):611-631
18. Pflug GC (2000) Some remarks on the value-at-risk and the conditional value-at-risk. In: Uryasev S(eds) Probabilistic constrained optimization: Methodology and optimization. Kluwer, Norwell, pp 278-287
19. Rockafellar RT (1970) Convex analysis. Princeton University Press, Englewood Cliffs
20. Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21-41
21. Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distribution. J Banking Financ 26:1443-1471
22. Pham Dinh T, Le Thi HA (1997) Convex analysis approach to DC programming: Theory, algorithms and applications. Acta Math Vietnamica, dedicated to Professor Hoang Tuy on the occasion of his 70th birthday 22(1):289-355
23. Pham Dinh T, Le Thi HA (1998) DC optimization algorithms for solving the trust region subproblem. SIAM J Optim 8: 476-505