메뉴 건너뛰기




Volumn 129, Issue 2, 2011, Pages 357-382

Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems

Author keywords

Approximation algorithms; Convex programming; Diameters of convex bodies; Polynomial optimization

Indexed keywords

APPROXIMATION BOUNDS; CARTESIAN PRODUCTS; CONVEX BODY; CONVEX PROGRAMMING; DETERMINISTIC APPROXIMATION; HOMOGENEOUS POLYNOMIALS; MULTILINEAR FORMS; MULTIQUADRATICS; POLYNOMIAL OPTIMIZATION; POLYNOMIAL OPTIMIZATION PROBLEM;

EID: 81155134640     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0464-0     Document Type: Article
Times cited : (53)

References (31)
  • 1
    • 34250182060 scopus 로고    scopus 로고
    • Integration and optimization of multivariate polynomials by restriction onto a random subspace
    • Barvinok, A.: Integration and optimization of multivariate polynomials by restriction onto a random subspace. Found. Comput. Math. 7(2), 229-244 (2007)
    • (2007) Found. Comput. Math. , vol.7 , Issue.2 , pp. 229-244
    • Barvinok, A.1
  • 2
    • 21144446845 scopus 로고    scopus 로고
    • Deterministic and randomized polynomial-time approximation of RADII
    • Brieden, A., Gritzmann, P., Kannan, R., Klee, V., Lovász, L., Simonovits, M.: Deterministic and randomized polynomial-time approximation of radii. Mathematika 48, 63-105 (2001) (Pubitemid 33745484)
    • (2001) Mathematika , vol.48 , Issue.1-2 , pp. 63-105
    • Brieden, A.1    Gritzmann, P.2    Kannan, R.3    Klee, V.4    Lovasz, L.5    Simonovits, M.6
  • 3
    • 0004236492 scopus 로고    scopus 로고
    • 3rd edn. The Johns Hopkins University Press, Baltimore
    • Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 4
    • 0000012770 scopus 로고
    • Inner and outer j -radii of convex bodies in finite-dimensional normed spaces
    • Gritzmann, P., Klee, V.: Inner and outer j -radii of convex bodies in finite-dimensional normed spaces. Discret. Comput. Geom. 7(1), 255-280 (1992)
    • (1992) Discret. Comput. Geom. , vol.7 , Issue.1 , pp. 255-280
    • Gritzmann, P.1    Klee, V.2
  • 5
    • 0006362327 scopus 로고
    • Geometric algorithms and combinatorial optimization
    • 2nd corrected edn. Springer, Berlin
    • Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics, vol. 2, 2nd corrected edn. Springer, Berlin (1993)
    • (1993) Algorithms and Combinatorics , vol.2
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 6
    • 65649110856 scopus 로고    scopus 로고
    • Conditions for strong ellipticity of anisotropic elastic materials
    • Han, D., Dai, H.H., Qi, L.: Conditions for strong ellipticity of anisotropic elastic materials. J. Elast. 97(1), 1-13 (2009)
    • (2009) J. Elast. , vol.97 , Issue.1 , pp. 1-13
    • Han, D.1    Dai, H.H.2    Qi, L.3
  • 7
    • 81155155956 scopus 로고    scopus 로고
    • Technical Report of SEEM2009-06, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong
    • He, S., Li, Z., Zhang, S.: General constrained polynomial optimization: an approximation approach. Technical Report of SEEM2009-06, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong (2009)
    • (2009) General Constrained Polynomial Optimization: An Approximation Approach
    • He, S.1    Li, Z.2    Zhang, S.3
  • 8
    • 77958088475 scopus 로고    scopus 로고
    • Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
    • He, S., Li, Z., Zhang, S.: Approximation algorithms for homogeneous polynomial optimization with quadratic constraints. Math. Program. Ser. B 125(2), 353-383 (2010)
    • (2010) Math. Program. Ser. B , vol.125 , Issue.2 , pp. 353-383
    • He, S.1    Li, Z.2    Zhang, S.3
  • 10
    • 80051813983 scopus 로고    scopus 로고
    • On the best low multilinear rank approximation of higher-order tensors
    • Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds.), Springer, Berlin
    • Ishteva, M., Absil, P.A., van Huffel, S., de Lathauwer, L. : On the best low multilinear rank approximation of higher-order tensors. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds.) Recent Advances in Optimization and its Applications in Engineering, pp. 145-164. Springer, Berlin (2010)
    • (2010) Recent Advances in Optimization and its Applications in Engineering , pp. 145-164
    • Ishteva, M.1    Absil, P.A.2    Van Huffel, S.3    De Lathauwer, L.4
  • 12
    • 55249099801 scopus 로고    scopus 로고
    • Linear equations modulo 2 and the L1 diameter of convex bodies
    • Khot, S., Naor, A.: Linear equations modulo 2 and the L1 diameter of convex bodies. SIAM J. Comput. 38(4), 1448-1463 (2008)
    • (2008) SIAM J. Comput. , vol.38 , Issue.4 , pp. 1448-1463
    • Khot, S.1    Naor, A.2
  • 13
    • 44349154854 scopus 로고    scopus 로고
    • The complexity of optimizing over a simplex, hypercube or sphere: A short survey
    • de Klerk, E.: The complexity of optimizing over a simplex, hypercube or sphere: A short survey. Cent. Eur. J. Oper. Res. 16(2), 111-125 (2008)
    • (2008) Cent. Eur. J. Oper. Res. , vol.16 , Issue.2 , pp. 111-125
    • De Klerk, E.1
  • 14
    • 33646746975 scopus 로고    scopus 로고
    • A PTAS for the minimization of polynomials of fixed degree over the simplex
    • DOI 10.1016/j.tcs.2006.05.011, PII S0304397506003252
    • de Klerk, E., Laurent, M., Parrilo, P.A.: A PTAS for the minimization of polynomials of fixed degree over the simplex. Theor. Comput. Sci. 361(2-3), 210-225 (2006) (Pubitemid 44189105)
    • (2006) Theoretical Computer Science , vol.361 , Issue.2-3 , pp. 210-225
    • De Klerk, E.1    Laurent, M.2    Parrilo, P.A.3
  • 16
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455-500 (2009)
    • (2009) SIAM Rev. , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 17
    • 0009187121 scopus 로고
    • Decoupling inequalities for polynomial chaos
    • Kwapien, S.: Decoupling inequalities for polynomial chaos. Ann. Probab. 15(3), 1062-1071 (1987)
    • (1987) Ann. Probab. , vol.15 , Issue.3 , pp. 1062-1071
    • Kwapien, S.1
  • 18
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre, J.B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796-817 (2001)
    • (2001) SIAM J. Optim. , vol.11 , Issue.3 , pp. 796-817
    • Lasserre, J.B.1
  • 19
    • 67349148256 scopus 로고    scopus 로고
    • Sums of squares, moment matrices and optimization over polynomials
    • Putinar, M., Sullivant, S. (eds.), Springer Science+Business Media, LLC, New York
    • Laurent, M.: Sums of squares, moment matrices and optimization over polynomials. In: Putinar, M., Sullivant, S. (eds.) Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and Its Applications, vol. 149, pp. 157-270. Springer Science+Business Media, LLC, New York (2009)
    • (2009) Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and Its Applications , vol.149 , pp. 157-270
    • Laurent, M.1
  • 20
    • 77956009889 scopus 로고    scopus 로고
    • Multiarray signal processing: Tensor decomposition meets compressed sensing
    • Lim, L.H., Comon, P.: Multiarray signal processing: tensor decomposition meets compressed sensing. Comptes Rendus Mécanique 338(6), 311-320 (2010)
    • (2010) Comptes Rendus Mécanique , vol.338 , Issue.6 , pp. 311-320
    • Lim, L.H.1    Comon, P.2
  • 21
    • 73249147288 scopus 로고    scopus 로고
    • Biquadratic optimization over unit spheres and semidefinite programming relaxations
    • Ling, C., Nie, J., Qi, L., Ye, Y.: Biquadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J. Optim. 20(3), 1286-1310 (2009)
    • (2009) SIAM J. Optim. , vol.20 , Issue.3 , pp. 1286-1310
    • Ling, C.1    Nie, J.2    Qi, L.3    Ye, Y.4
  • 22
    • 77951288110 scopus 로고    scopus 로고
    • A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraints
    • Luo, Z.Q., Zhang, S.: A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraints. SIAM J. Optim. 20(4), 1716-1736 (2010)
    • (2010) SIAM J. Optim. , vol.20 , Issue.4 , pp. 1716-1736
    • Luo, Z.Q.1    Zhang, S.2
  • 23
    • 77952093279 scopus 로고    scopus 로고
    • Random walk in a simplex and quadratic optimization over convex polytopes
    • Université Catholique de Louvain, Belgium
    • Nesterov, Yu.: Random walk in a simplex and quadratic optimization over convex polytopes. CORE Discussion Paper 2003071, Université Catholique de Louvain, Belgium (2003)
    • (2003) CORE Discussion Paper 2003071
    • Nesterov, Yu.1
  • 24
    • 81155141615 scopus 로고    scopus 로고
    • An approximation bound analysis for Lasserre's relaxation in multivariate polynomial optimization
    • Nie, J.: An approximation bound analysis for Lasserre's relaxation in multivariate polynomial optimization (2009, Preprint)
    • (2009) Preprint
    • Nie, J.1
  • 26
    • 27744582534 scopus 로고    scopus 로고
    • Eigenvalues of a real supersymmetric tensor
    • DOI 10.1016/j.jsc.2005.05.007, PII S0747717105000817
    • Qi, L.: Eigenvalues of a real supersymmetric tensor. J. Symbol. Comput. 40(6), 1302-1324 (2005) (Pubitemid 41600816)
    • (2005) Journal of Symbolic Computation , vol.40 , Issue.6 , pp. 1302-1324
    • Qi, L.1
  • 27
    • 63949087720 scopus 로고    scopus 로고
    • Conditions for strong ellipticity and M-Eigenvalues
    • Qi, L., Dai, H.H., Han, D.: Conditions for strong ellipticity and M-Eigenvalues. Front. Math. China 4(2), 349-364 (2009)
    • (2009) Front. Math. China , vol.4 , Issue.2 , pp. 349-364
    • Qi, L.1    Dai, H.H.2    Han, D.3
  • 28
    • 58149504770 scopus 로고    scopus 로고
    • Z-Eigenvaluemethods for a global polynomial optimization problem
    • Qi, L.,Wang, F.,Wang,Y.: Z-Eigenvaluemethods for a global polynomial optimization problem.Math. Program. Ser. A 118(2), 301-316 (2009)
    • (2009) Math. Program. Ser. A , vol.118 , Issue.2 , pp. 301-316
    • Qi, L.1    Wang, F.2    Wang, Y.3
  • 29
    • 0001157581 scopus 로고    scopus 로고
    • Some concrete aspects of Hilbert's 17th problem
    • Delzell, C.N., Madden, J.J. (eds.), American Mathematical Society, Providence Rhode Island
    • Reznick,B.: Some concrete aspects of Hilbert's 17th problem. In: Delzell, C.N., Madden, J.J. (eds.) Real Algebraic Geometry and Ordered Structures, Contemporary Mathematics, vol. 253, pp. 251-272. American Mathematical Society, Providence Rhode Island (2000)
    • (2000) Real Algebraic Geometry and Ordered Structures, Contemporary Mathematics , vol.253 , pp. 251-272
    • Reznick, B.1
  • 30
    • 61449210981 scopus 로고    scopus 로고
    • A unified theorem on SDP rank reduction
    • So, A.M.C., Ye, Y., Zhang, J.: A unified theorem on SDP rank reduction. Math. Oper. Res. 33(4), 910-920 (2008)
    • (2008) Math. Oper. Res. , vol.33 , Issue.4 , pp. 910-920
    • So, A.M.C.1    Ye, Y.2    Zhang, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.