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Original Articles

SDP vs. LP Relaxations for the Moment Approach in Some Performance Evaluation Problems

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Pages 439-456 | Received 01 Jun 2003, Published online: 16 Feb 2007

References

  • Helmes , K. , Röhl , S. and Stockbridge , R.H. 2001 . Computing moments of the exit time distribution for Markov processes by linear programming . Oper. Res. , 49 : 516 – 530 .
  • Stockbridge , R.H. 1990 . Time-average control of martingale problems: Existence of a stationary solution . Ann. Probab. , 18 : 190 – 205 .
  • Stockbridge , R.H. 1990 . Time-average control of martingale problems: A linear programming formulation . Ann. Probab. , 18 : 206 – 217 .
  • Kurtz , T.G. , Stockbridge , R.H. and Richard , H. 2001 . Stationary solutions and forward equations for controlled and singular martingale problems . Electronic J. Probab. , 6 Paper No. 17
  • Ethier , S.N. and Kurtz , T.G. 1986 . Markov Processes: Characterization and Convergence New York : John Wiley .
  • Dawson , D.A. 1978 . Geostochastic calculus . Can. J. Statist. , 6 : 143 – 168 .
  • Dawson , D.A. 1980 . Qualitative behaviour of geostochastic systems . Stoch. Proc. Appl. , 10 : 1 – 31 . [CROSSREF]
  • Feller , W. 1965 . An Introduction to Probability Theory and Its Applications Vol. 2 , New York : John Wiley .
  • Shohat , J. and Tamarkin , J. 1943 . The Problem of Moments , 1st Providence, RI : American Mathematical Society .
  • Vandenberghe , L. and Boyd , S. 1996 . Semidefinite programming . SIAM Rev. , 38 : 49 – 95 .
  • Schwerer , E. 2001 . A linear programming approach to the steady-state analysis of reflected Brownian motion . Stoch. Models , 17 : 341 – 368 . [CROSSREF]
  • Lovász , L. and Schrijver , A. 1991 . Cones of matrices and set-functions and 0–1 optimization . SIAM J. Optim. , 1 : 166 – 190 .
  • Lasserre , J.B. 2002 . An equivalent positive semidefinite program for non-linear 0–1 programs . SIAM J. Optim. , 12 : 756 – 769 . [CROSSREF]
  • Kurtz , T.G. and Stockbridge , R.H. 1998 . Existence of Markov controls and characterization of optimal Markov controls . SIAM J. Control Optim. , 36 : 609 – 653 . [CROSSREF]
  • Putinar , M. 1993 . Positive polynomials on compact semi-algebraic sets . Ind. Univ. J. , 42 : 969 – 984 .
  • Curto , R.E. and Fialkow , L.A. 1991 . Recursiveness, positivity and truncated moment problems . Houston J. Math. , 17 : 603 – 635 .
  • Lasserre , J.B. 2002 . Semidefinite programming vs. LP relaxations for polynomial programming . Math. Oper. Res. , 27 : 347 – 360 . [CROSSREF]
  • Sturm , J.S. 1999 . Using SeDuMi, a Matlab toolbox for optimization over symmetric cones (updated for Version 1.05) . Optim. Methods Softw. , 11–12 : 625 – 653 .
  • Baxter , M.W. and Rennie , A.J.O. 1993 . Financial Calculus Cambridge : Cambridge University Press .
  • Srivastava , M.S. and Wu , Y. 1994 . Dynamic sampling plan in Shiryaev-Roberts procedure for detecting a change in the drift of Brownian motion . Ann. Statis. , 22 : 805 – 823 .
  • Lasserre , J.B. , Prieto-Rumeau , T. and Zervos , M. Pricing a class of exotic options via moments and SDP relaxations. LAAS Report No. 03391. Submitted 2003

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