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Volumn 112, Issue 1, 2008, Pages 65-92

A semidefinite programming approach to the generalized problem of moments

Author keywords

Problem of moments; Relaxations; Semidefinite programming

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL PROGRAMMING; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING;

EID: 34547470409     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0085-1     Document Type: Conference Paper
Times cited : (111)

References (40)
  • 2
    • 0003292618 scopus 로고
    • Some questions in the theory of moments
    • Am. Math. Soc., Providence, R.I.
    • Akhiezer, N.I., Krein, M.G.: Some questions in the theory of moments. Am. Math. Soc. Transl. 2, Am. Math. Soc., Providence, R.I. (1962)
    • (1962) Am. Math. Soc. Transl. , vol.2
    • Akhiezer, N.I.1    Krein, M.G.2
  • 3
    • 0040241930 scopus 로고
    • Moments in probability theory and approximation theory
    • Longman Scientific & Technical
    • Anastassiou, G.A.: Moments in Probability Theory and Approximation Theory, Pitman Research Notes in Mathematics Series. Longman Scientific & Technical (1993)
    • (1993) Pitman Research Notes in Mathematics Series
    • Anastassiou, G.A.1
  • 6
    • 0000913894 scopus 로고
    • The multidimensional moment problem and semi-groups
    • Landau, H.J. (ed.) Moments in Mathematics. American Mathematical Society, Providence
    • Berg, C.: The multidimensional moment problem and semi-groups. In: Landau, H.J. (ed.) Moments in Mathematics. American Mathematical Society, Providence. Proc. Symp. Appl. Math. 37, 110-124 (1980)
    • (1980) Proc. Symp. Appl. Math. , vol.37 , pp. 110-124
    • Berg, C.1
  • 7
    • 23844499733 scopus 로고    scopus 로고
    • Optimal inequalities in probability theory: A convex optimization approach
    • Bertsimas D. and Popescu I. (2005). Optimal inequalities in probability theory: a convex optimization approach. SIAM J. Optim. 15: 780-804
    • (2005) SIAM J. Optim. , vol.15 , pp. 780-804
    • Bertsimas, D.1    Popescu, I.2
  • 8
    • 0000825922 scopus 로고
    • Recursiveness, positivity, and truncated moment problems
    • Curto R.E. and Fialkow L.A. (1991). Recursiveness, positivity and truncated moment problems. Houston J. Math. 17: 603-635
    • (1991) Houston J. Math. , vol.17 , pp. 603-635
    • Curto, R.E.1    Fialkow, L.A.2
  • 9
    • 23044517911 scopus 로고    scopus 로고
    • The truncated complex K-moment problem
    • Curto R.E. and Fialkow L.A. (2000). The truncated complex K-moment problem. Trans. Am. Math. Soc. 352: 2825-2855
    • (2000) Trans. Am. Math. Soc. , vol.352 , pp. 2825-2855
    • Curto, R.E.1    Fialkow, L.A.2
  • 10
    • 2542587541 scopus 로고    scopus 로고
    • GloptiPoly:global optimization over polynomials with matlab and SeDuMi
    • Henrion D. and Lasserre J.B. (2003). GloptiPoly:global optimization over polynomials with matlab and SeDuMi. ACM Trans. Math. Soft. 29: 165-194
    • (2003) ACM Trans. Math. Soft. , vol.29 , pp. 165-194
    • Henrion, D.1    Lasserre, J.B.2
  • 12
    • 0013249284 scopus 로고    scopus 로고
    • Approximation schemes for infinite linear programs
    • Hernández-Lerma O. and Lasserre J.B. (1998). Approximation schemes for infinite linear programs. SIAM J. Optim. 8: 973-988
    • (1998) SIAM J. Optim. , vol.8 , pp. 973-988
    • Hernández-Lerma, O.1    Lasserre, J.B.2
  • 13
    • 0009578965 scopus 로고
    • The extrema of probability determined by generalized moments (I): Bounded random variables
    • Isii K. (1960). The extrema of probability determined by generalized moments (I): bounded random variables. Ann. Inst. Math. Stat. 12: 119-133
    • (1960) Ann. Inst. Math. Stat. , vol.12 , pp. 119-133
    • Isii, K.1
  • 14
    • 0001315224 scopus 로고
    • On sharpness of Tchebycheff-type inequalities
    • Isii K. (1963). On sharpness of Tchebycheff-type inequalities. Ann. Inst. Stat. Math. 14: 185-197
    • (1963) Ann. Inst. Stat. Math. , vol.14 , pp. 185-197
    • Isii, K.1
  • 15
    • 0035531030 scopus 로고    scopus 로고
    • Distinguished representations of strictly positive polynomials
    • Jacobi T. and Prestel A. (2001). Distinguished representations of strictly positive polynomials. J. Reine. Angew. Math. 532: 223-235
    • (2001) J. Reine. Angew. Math. , vol.532 , pp. 223-235
    • Jacobi, T.1    Prestel, A.2
  • 16
    • 29144520191 scopus 로고    scopus 로고
    • Global optimization of rational functions: A semidefinite programming approach
    • Jibetean D. and de Klerk E. (2006). Global optimization of rational functions: a semidefinite programming approach. Math. Prog. A 106: 93-109
    • (2006) Math. Prog. A , vol.106 , pp. 93-109
    • Jibetean, D.1    De Klerk, E.2
  • 18
    • 0002471618 scopus 로고
    • Geometry of the moment problem
    • Landau, H.J. (ed.) Moments in Mathematics, American Mathematical Society, Providence
    • Kemperman, J.H.B.: Geometry of the moment problem, In: Landau, H.J. (ed.) Moments in Mathematics, American Mathematical Society, Providence. Proc. Symp. Appl. Math. 37, 16-53 (1980)
    • (1980) Proc. Symp. Appl. Math. , vol.37 , pp. 16-53
    • Kemperman, J.H.B.1
  • 19
    • 0003197687 scopus 로고
    • Markov moment problems and extremal problems
    • Translations of Am. Math. Soc., Providence, RI
    • Krein, M.G., Nudelman, A.A.: Markov Moment Problems and Extremal Problems. Translations of Math. Monographs vol. 50, Am. Math. Soc., Providence, RI (1977)
    • (1977) Math. Monographs , vol.50
    • Krein, M.G.1    Nudelman, A.A.2
  • 20
    • 0003372433 scopus 로고
    • Moments in mathematics
    • Landau, H.J. (ed.) American Mathematical Society, Providence
    • Landau, H.J.: Moments in mathematics. In: Landau, H.J. (ed.) Proc. Symp. Appl. Math. 37, American Mathematical Society, Providence (1980)
    • (1980) Proc. Symp. Appl. Math. , vol.37
    • Landau, H.J.1
  • 21
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre J.B. (2001). Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11: 796-817
    • (2001) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 22
    • 0036351765 scopus 로고    scopus 로고
    • An explicit equivalent positive semidefinite program for nonlinear 0-1 programs
    • Lasserre J.B. (2002). An explicit equivalent positive semidefinite program for nonlinear 0-1 programs. SIAM J. Optim. 12: 756-769
    • (2002) SIAM J. Optim. , vol.12 , pp. 756-769
    • Lasserre, J.B.1
  • 23
    • 0036387295 scopus 로고    scopus 로고
    • Bounds on measures satisfying moment conditions
    • Lasserre J.B. (2002). Bounds on measures satisfying moment conditions. Ann. Appl. Prob. 12: 1114-1137
    • (2002) Ann. Appl. Prob. , vol.12 , pp. 1114-1137
    • Lasserre, J.B.1
  • 27
    • 33745011879 scopus 로고    scopus 로고
    • Option pricing exotic options via moments and semidefinite relaxations
    • Lasserre J.B., Prieto-Rumeau T. and Zervos M. (2006). Option pricing exotic options via moments and semidefinite relaxations. Math. Financ. 16: 469-494
    • (2006) Math. Financ. , vol.16 , pp. 469-494
    • Lasserre, J.B.1    Prieto-Rumeau, T.2    Zervos, M.3
  • 28
    • 34547492080 scopus 로고    scopus 로고
    • Convergent semidefinite relaxations in polynomial optimization with sparsity
    • Lasserre J.B. (2006). Convergent semidefinite relaxations in polynomial optimization with sparsity. SIAM J. Optim. 17: 822-843
    • (2006) SIAM J. Optim. , vol.17 , pp. 822-843
    • Lasserre, J.B.1
  • 29
    • 26444549416 scopus 로고    scopus 로고
    • Revisiting two theorems of Curto and Fialkow on moment matrices
    • Laurent M. (2005). Revisiting two theorems of Curto and Fialkow on moment matrices. Proc. Amer. Math. Soc. 133: 2965-2976
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2965-2976
    • Laurent, M.1
  • 30
    • 84972537501 scopus 로고
    • Exponentially bounded positive definite functions
    • Maserick P.H. and Berg C. (1984). Exponentially bounded positive definite functions. Illinois J. Math. 28: 162-179
    • (1984) Illinois J. Math. , vol.28 , pp. 162-179
    • Maserick, P.H.1    Berg, C.2
  • 31
    • 0000939331 scopus 로고
    • Quasi-analytic vectors
    • Nussbaum A.E. (1966). Quasi-analytic vectors. Ark. Mat. 6: 179-191
    • (1966) Ark. Mat. , vol.6 , pp. 179-191
    • Nussbaum, A.E.1
  • 32
    • 23044523312 scopus 로고    scopus 로고
    • Polynomials that are positive on an interval
    • Powers V. and Reznick B. (2000). Polynomials that are positive on an interval. Trans. Am. math. Soc. 352: 4677-4692
    • (2000) Trans. Am. Math. Soc. , vol.352 , pp. 4677-4692
    • Powers, V.1    Reznick, B.2
  • 33
    • 0013043479 scopus 로고
    • On the relation between the multidimensional moment problem and the one dimensional moment problem
    • Petersen L.C. (1982). On the relation between the multidimensional moment problem and the one dimensional moment problem. Math. Scand. 51: 361-366
    • (1982) Math. Scand. , vol.51 , pp. 361-366
    • Petersen, L.C.1
  • 34
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar M. (1993). Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42: 969-984
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 35
    • 0001250675 scopus 로고
    • The K-moment problem for compact semi-algebraic sets
    • Schmüdgen K. (1991). The K-moment problem for compact semi-algebraic sets. Math. Ann. 289: 203-206
    • (1991) Math. Ann. , vol.289 , pp. 203-206
    • Schmüdgen, K.1
  • 36
    • 23844493105 scopus 로고    scopus 로고
    • Optimization of polynomials on compact semialgebraic sets
    • Schweighofer M. (2005). Optimization of polynomials on compact semialgebraic sets. SIAM J. Optim. 15: 805-825
    • (2005) SIAM J. Optim. , vol.15 , pp. 805-825
    • Schweighofer, M.1
  • 38
    • 0002672593 scopus 로고    scopus 로고
    • The classical moment problem as a self-adjoint finite difference operator
    • Simon B. (1998). The classical moment problem as a self-adjoint finite difference operator. Adv. Math. 137: 82-203
    • (1998) Adv. Math. , vol.137 , pp. 82-203
    • Simon, B.1
  • 39
    • 0027556195 scopus 로고
    • Convex duality and nonlinear optimal control
    • Vinter V. (1993). Convex duality and nonlinear optimal control. SIAM J. Control Optim. 31: 518-538
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 518-538
    • Vinter, V.1
  • 40
    • 33847158335 scopus 로고    scopus 로고
    • Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity
    • Waki S., Kim S., Kojima M. and Maramatsu M. (2006). Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity. SIAM J. Optim. 17: 218-242
    • (2006) SIAM J. Optim. , vol.17 , pp. 218-242
    • Waki, S.1    Kim, S.2    Kojima, M.3    Maramatsu, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.