메뉴 건너뛰기




Volumn 7, Issue 2, 2012, Pages 321-346

Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces

Author keywords

Approximation bound; form; G norm; hypersurface; L 2 norm; multi form; polynomial; semidefinite programming; sum of squares

Indexed keywords


EID: 84858438014     PISSN: 16733452     EISSN: 16733576     Source Type: Journal    
DOI: 10.1007/s11464-012-0187-4     Document Type: Article
Times cited : (33)

References (14)
  • 1
    • 33748567127 scopus 로고    scopus 로고
    • There are significantly more nonnegative polynomials than sums of squares
    • Blekherman G. There are significantly more nonnegative polynomials than sums of squares. Israel J Math, 2006, 153: 355-380.
    • (2006) Israel J Math , vol.153 , pp. 355-380
    • Blekherman, G.1
  • 2
    • 33746906690 scopus 로고    scopus 로고
    • Global optimization of homogeneous polynomials on the simplex and on the sphere. Frontiers in Global Optimization
    • C. Floudas and P. Pardalos (Eds.), Boston: Kluwer Academic Publishers
    • Faybusovich L. Global optimization of homogeneous polynomials on the simplex and on the sphere. In: Floudas C, Pardalos P, eds. Frontiers in Global Optimization. Nonconvex Optim Appl, Vol 74. Boston: Kluwer Academic Publishers, 2004, 109-121.
    • (2004) Nonconvex Optim Appl , vol.74 , pp. 109-121
    • Faybusovich, L.1
  • 3
    • 0007025424 scopus 로고
    • Über den Vergleich des arithmetischen und des geometrischen
    • Hurwitz A. Über den Vergleich des arithmetischen und des geometrischen. Mittels J Reine Angew Math, 1891, 108: 266-268.
    • (1891) Mittels J Reine Angew Math , vol.108 , pp. 266-268
    • Hurwitz, A.1
  • 4
    • 17444428545 scopus 로고    scopus 로고
    • Sparsity in sums of squares of polynomials
    • Kojima M, Kim S, Waki H. Sparsity in sums of squares of polynomials. Math Program, 2005, 103(1): 45-62.
    • (2005) Math Program , vol.103 , Issue.1 , pp. 45-62
    • Kojima, M.1    Kim, S.2    Waki, H.3
  • 5
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre J. Global optimization with polynomials and the problem of moments. SIAM J Optim, 2001, 11(3): 796-817.
    • (2001) SIAM J Optim , vol.11 , Issue.3 , pp. 796-817
    • Lasserre, J.1
  • 6
    • 73249147288 scopus 로고    scopus 로고
    • Bi-quadratic optimization over unit spheres and semidefinite programming relaxations
    • Ling C, Nie J, Qi L, Ye Y. Bi-quadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J Optim, 2009, 20(3): 1286-1310.
    • (2009) SIAM J Optim , vol.20 , Issue.3 , pp. 1286-1310
    • Ling, C.1    Nie, J.2    Qi, L.3    Ye, Y.4
  • 8
    • 70450210375 scopus 로고    scopus 로고
    • Sparse SOS relaxations for minimizing functions that are summations of small polynomials
    • Nie J, Demmel J. Sparse SOS relaxations for minimizing functions that are summations of small polynomials. SIAM J Optim, 2008, 19(4): 1534-1558.
    • (2008) SIAM J Optim , vol.19 , Issue.4 , pp. 1534-1558
    • Nie, J.1    Demmel, J.2
  • 9
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite Programming relaxations for semialgebraic problems
    • Parrilo P. Semidefinite Programming relaxations for semialgebraic problems. Math Program, Ser B, 2003, 96(2): 293-320.
    • (2003) Math Program, Ser B , vol.96 , Issue.2 , pp. 293-320
    • Parrilo, P.1
  • 10
    • 85128577150 scopus 로고    scopus 로고
    • In: Proceedings for the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003
    • Parrilo P. Exploiting structure in sum of squares programs. In: Proceedings for the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003. 2004, 4664-4669.
    • (2004) Exploiting structure in sum of squares programs , pp. 4664-4669
    • Parrilo, P.1
  • 12
    • 34249965956 scopus 로고
    • Forms derived from the arithmetic-geometric inequality
    • Reznick B. Forms derived from the arithmetic-geometric inequality. Math Ann, 1989, 283: 431-464.
    • (1989) Math Ann , vol.283 , pp. 431-464
    • Reznick, B.1
  • 13
    • 0001157581 scopus 로고    scopus 로고
    • th problem
    • Providence: Amer Math Soc
    • th problem. In: Contem Math, Vol 253. Providence: Amer Math Soc, 2000, 251-272.
    • (2000) Contem Math , vol.253 , pp. 251-272
    • Reznick, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.