메뉴 건너뛰기




Volumn 2, Issue 2, 2014, Pages 143-170

Conditional Quadratic Semidefinite Programming: Examples and Methods

Author keywords

Conditional semidefinite programming; Euclidean distance matrix; Matrix optimization; Semismooth Newton method

Indexed keywords

COMPUTER APPLICATIONS; OPERATIONS RESEARCH;

EID: 84903600117     PISSN: 2194668X     EISSN: 21946698     Source Type: Journal    
DOI: 10.1007/s40305-014-0048-9     Document Type: Review
Times cited : (7)

References (49)
  • 1
    • 0002740666 scopus 로고    scopus 로고
    • Solving Euclidean distance matrix completion problems via semidefinite programming
    • Alfakih, A. Y., Khandani, A., Wolkowicz, H.: Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl. 12, 13-30 (1999).
    • (1999) Comput. Optim. Appl. , vol.12 , pp. 13-30
    • Alfakih, A.Y.1    Khandani, A.2    Wolkowicz, H.3
  • 3
    • 33745879331 scopus 로고
    • Conditionally positive functions and p-norm distance matrices
    • Baxter, B. J. C.: Conditionally positive functions and p-norm distance matrices. Constr. Approx. 7, 427-440 (1991).
    • (1991) Constr. Approx. , vol.7 , pp. 427-440
    • Baxter, B.J.C.1
  • 6
    • 0038485144 scopus 로고    scopus 로고
    • Analysis of nonsmooth symmetric matrix valued functions with applications to semidefinite complementarity problems
    • Chen, X., Qi, H.-D., Tseng, P.: Analysis of nonsmooth symmetric matrix valued functions with applications to semidefinite complementarity problems. SIAM J. Optim. 13, 960-985 (2003).
    • (2003) SIAM J. Optim. , vol.13 , pp. 960-985
    • Chen, X.1    Qi, H.-D.2    Tseng, P.3
  • 7
    • 0001499369 scopus 로고
    • Definiteness and semidefiniteness of quadratic forms revisted
    • Chabrillac, Y., Crouzeix, J.-P.: Definiteness and semidefiniteness of quadratic forms revisted. Linear Algebra Appl. 63, 283-292 (1984).
    • (1984) Linear Algebra Appl. , vol.63 , pp. 283-292
    • Chabrillac, Y.1    Crouzeix, J.-P.2
  • 8
    • 58049197110 scopus 로고    scopus 로고
    • Constraint nondegeneracy, strong regularity and nonsingularity in semidefinite programming
    • Chan, Z. X., Sun, D. F.: Constraint nondegeneracy, strong regularity and nonsingularity in semidefinite programming. SIAM J. Optim. 19, 370-396 (2008).
    • (2008) SIAM J. Optim. , vol.19 , pp. 370-396
    • Chan, Z.X.1    Sun, D.F.2
  • 13
    • 0001886656 scopus 로고
    • A cyclic projection algorithm via duality
    • Gaffke, N., Mathar, R.: A cyclic projection algorithm via duality. Metrika 36, 29-54 (1989).
    • (1989) Metrika , vol.36 , pp. 29-54
    • Gaffke, N.1    Mathar, R.2
  • 15
    • 84861325244 scopus 로고    scopus 로고
    • Calibrating least squares covariance matrix problems with equality and inequality constraints
    • Gao, Y., Sun, D. F.: Calibrating least squares covariance matrix problems with equality and inequality constraints. SIAM J. Matrix Anal. Appl. 31, 1432-1457 (2009).
    • (2009) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 1432-1457
    • Gao, Y.1    Sun, D.F.2
  • 16
    • 0000771519 scopus 로고
    • An alternating projection algorithm for computing the nearest Euclidean distance matrix
    • Glunt, W., Hayden, T. L., Hong, S., Wells, J.: An alternating projection algorithm for computing the nearest Euclidean distance matrix. SIAM J. Matrix Anal. Appl. 11, 589-600 (1990).
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 589-600
    • Glunt, W.1    Hayden, T.L.2    Hong, S.3    Wells, J.4
  • 17
    • 0025986584 scopus 로고
    • The embedding problem for predistance matrices
    • Glunt, W., Hayden, T. L., Liu, W.-M.: The embedding problem for predistance matrices. Bull. Math. Biol. 53, 769-796 (1991).
    • (1991) Bull. Math. Biol. , vol.53 , pp. 769-796
    • Glunt, W.1    Hayden, T.L.2    Liu, W.-M.3
  • 18
    • 0000922470 scopus 로고
    • Molecular conformations from distance matrices
    • Glunt, W., Hayden, T. L., Raydan, R.: Molecular conformations from distance matrices. J. Comput. Chem. 14, 114-120 (1993).
    • (1993) J. Comput. Chem. , vol.14 , pp. 114-120
    • Glunt, W.1    Hayden, T.L.2    Raydan, R.3
  • 19
    • 0000071395 scopus 로고
    • Some distance properties of latent root and vector methods in multivariate analysis
    • Gower, J. C.: Some distance properties of latent root and vector methods in multivariate analysis. Biometrika 53, 315-328 (1966).
    • (1966) Biometrika , vol.53 , pp. 315-328
    • Gower, J.C.1
  • 20
    • 68149166355 scopus 로고    scopus 로고
    • Molecular embedding via a second order dissimilarity parameterized approach
    • Grooms, I. G., Lewis, R. M., Trosset, M. W.: Molecular embedding via a second order dissimilarity parameterized approach. SIAM J. Sci. Comput. 31, 2733-2756 (2009).
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 2733-2756
    • Grooms, I.G.1    Lewis, R.M.2    Trosset, M.W.3
  • 21
    • 0041904419 scopus 로고
    • Approximation by matrices positive semidefinite on a subspace
    • Hayden, T. L., Wells, J.: Approximation by matrices positive semidefinite on a subspace. Linear Algebra Appl. 109, 115-130 (1988).
    • (1988) Linear Algebra Appl. , vol.109 , pp. 115-130
    • Hayden, T.L.1    Wells, J.2
  • 22
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes, M. R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409-436 (1952).
    • (1952) J. Res. Natl. Bur. Stand. , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 23
    • 84903558371 scopus 로고
    • The solvability conditions for the inverse problem of matrices positive semidefinite on a subspace
    • Hu, X., Zhang, L., Du, W.: The solvability conditions for the inverse problem of matrices positive semidefinite on a subspace. J. Comput. Math. 12, 78-87 (1994).
    • (1994) J. Comput. Math. , vol.12 , pp. 78-87
    • Hu, X.1    Zhang, L.2    Du, W.3
  • 24
    • 10444271520 scopus 로고    scopus 로고
    • Conditionally definite matrices
    • Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya, Tematicheskie Obzory. Vol. 52, Algebra-9 (1998)
    • Ikramov, KhD, Savel'eva, N. V.: Conditionally definite matrices. J. Math. Sci. 98, 1-50 (2000). Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya, Tematicheskie Obzory. Vol. 52, Algebra-9 (1998).
    • (2000) J. Math. Sci. , vol.98 , pp. 1-50
    • Ikramov, K.D.1    Savel'eva, N.V.2
  • 25
    • 84867309078 scopus 로고    scopus 로고
    • An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP
    • Jiang, K., Sun, D. F., Toh, K.-C.: An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP. SIAM J. Optim. 22, 1042-1064 (2012).
    • (2012) SIAM J. Optim. , vol.22 , pp. 1042-1064
    • Jiang, K.1    Sun, D.F.2    Toh, K.-C.3
  • 26
    • 0034403710 scopus 로고    scopus 로고
    • The positive definite completion problem relative to a subspace
    • Johnson, C. R., Smith, R. L.: The positive definite completion problem relative to a subspace. Linear Algebra Appl. 307, 1-14 (2000).
    • (2000) Linear Algebra Appl. , vol.307 , pp. 1-14
    • Johnson, C.R.1    Smith, R.L.2
  • 28
    • 0040482135 scopus 로고
    • The best Euclidean fit to a given distance matrix in prescribed dimensions
    • Mathar, R.: The best Euclidean fit to a given distance matrix in prescribed dimensions. Linear Algebra Appl. 67, 1-6 (1985).
    • (1985) Linear Algebra Appl. , vol.67 , pp. 1-6
    • Mathar, R.1
  • 29
    • 34250122797 scopus 로고
    • Interpolation of scattered data: distance matrices and conditionally positive definite functions
    • Micchelli, C. A.: Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx. 2, 11-22 (1986).
    • (1986) Constr. Approx. , vol.2 , pp. 11-22
    • Micchelli, C.A.1
  • 33
    • 84877341941 scopus 로고    scopus 로고
    • A semismooth Newton method for the nearest Euclidean distance matrix problem
    • Qi, H.-D.: A semismooth Newton method for the nearest Euclidean distance matrix problem. SIAM J. Matrix Anal. Appl. 34, 67-93 (2013).
    • (2013) SIAM J. Matrix Anal. Appl. , vol.34 , pp. 67-93
    • Qi, H.-D.1
  • 34
    • 34247364678 scopus 로고    scopus 로고
    • A quadratically convergent Newton method for computing the nearest correlation matrix
    • Qi, H.-D., Sun, D. F.: A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM J. Matrix Anal. Appl. 28, 360-385 (2006).
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 360-385
    • Qi, H.-D.1    Sun, D.F.2
  • 35
    • 79953675385 scopus 로고    scopus 로고
    • An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem
    • Qi, H.-D., Sun, D. F.: An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem. IMA J. Numer. Anal. 31, 491-511 (2011).
    • (2011) IMA J. Numer. Anal. , vol.31 , pp. 491-511
    • Qi, H.-D.1    Sun, D.F.2
  • 36
    • 84865238482 scopus 로고    scopus 로고
    • A convex quadratic semidefinite programming approach to the partial additive constant problem in multidimensional scaling
    • Qi, H.-D., Xiu, N.: A convex quadratic semidefinite programming approach to the partial additive constant problem in multidimensional scaling. J. Stat. Comput. Simul. 82, 1317-1336 (2012).
    • (2012) J. Stat. Comput. Simul. , vol.82 , pp. 1317-1336
    • Qi, H.-D.1    Xiu, N.2
  • 37
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • Qi, L., Sun, J.: A nonsmooth version of Newton's method. Math. Program. 58, 353-367 (1993).
    • (1993) Math. Program. , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 38
    • 0039104820 scopus 로고    scopus 로고
    • Hadamard inverse, square roots and products of almost semidefinite matrices
    • Reams, R.: Hadamard inverse, square roots and products of almost semidefinite matrices. Linear Algebra Appl. 288, 35-43 (1999).
    • (1999) Linear Algebra Appl. , vol.288 , pp. 35-43
    • Reams, R.1
  • 40
    • 0001203499 scopus 로고
    • Remarks to Maurice Fréchet's article Sur la définition axiomatque d'une classe d'espaces vectoriels distanciés applicbles vectoriellement sur l'espace de Hilbet
    • Schoenberg, I. J.: Remarks to Maurice Fréchet's article "Sur la définition axiomatque d'une classe d'espaces vectoriels distanciés applicbles vectoriellement sur l'espace de Hilbet". Ann. Math. 36, 724-732 (1935).
    • (1935) Ann. Math. , vol.36 , pp. 724-732
    • Schoenberg, I.J.1
  • 41
    • 0001641319 scopus 로고
    • On certain metric spaces arising from Euclidean spaces by a change of metric and their embedding in Hilbert space
    • Schoenberg, I. J.: On certain metric spaces arising from Euclidean spaces by a change of metric and their embedding in Hilbert space. Ann. Math. 38(2), 787-793 (1937).
    • (1937) Ann. Math. , vol.38 , Issue.2 , pp. 787-793
    • Schoenberg, I.J.1
  • 42
    • 84968492782 scopus 로고
    • Metric spaces and positive definite functions
    • Schoenberg, I. J.: Metric spaces and positive definite functions. Trans. Am. Math. Soc. 44, 522-536 (1938).
    • (1938) Trans. Am. Math. Soc. , vol.44 , pp. 522-536
    • Schoenberg, I.J.1
  • 43
    • 0036474487 scopus 로고    scopus 로고
    • Semismooth matrix valued functions
    • Sun, D. F., Sun, J.: Semismooth matrix valued functions. Math. Oper. Res. 27, 150-169 (2002).
    • (2002) Math. Oper. Res. , vol.27 , pp. 150-169
    • Sun, D.F.1    Sun, J.2
  • 44
    • 34547439695 scopus 로고    scopus 로고
    • An inexact path-following algorithm for convex quadratic SDP
    • Toh, K. C.: An inexact path-following algorithm for convex quadratic SDP. Math. Program. 112, 221-254 (2008).
    • (2008) Math. Program. , vol.112 , pp. 221-254
    • Toh, K.C.1
  • 45
    • 84950351930 scopus 로고
    • Multidimensional scaling: I. Theory and method
    • Torgerson, W. S.: Multidimensional scaling: I. Theory and method. Psychometrka 17, 401-419 (1952).
    • (1952) Psychometrka , vol.17 , pp. 401-419
    • Torgerson, W.S.1
  • 47
    • 0034296096 scopus 로고    scopus 로고
    • Distance matrix completion by numerical optimization
    • Trosset, M. W.: Distance matrix completion by numerical optimization. Comput. Optim. Appl. 17, 11-22 (2000).
    • (2000) Comput. Optim. Appl. , vol.17 , pp. 11-22
    • Trosset, M.W.1
  • 48
    • 0002361037 scopus 로고
    • Discussion of a set of points in terms of their mutual distances
    • Young, G., Householder, A. S.: Discussion of a set of points in terms of their mutual distances. Psychometrika 3, 19-22 (1938).
    • (1938) Psychometrika , vol.3 , pp. 19-22
    • Young, G.1    Householder, A.S.2
  • 49
    • 77951274410 scopus 로고    scopus 로고
    • A Newton-CG augmented Lagrangian method for semidefinite programming
    • Zhao, X., Sun, D. F., Toh, K.-C.: A Newton-CG augmented Lagrangian method for semidefinite programming. SIAM J. Optim. 20, 1737-1765 (2010).
    • (2010) SIAM J. Optim. , vol.20 , pp. 1737-1765
    • Zhao, X.1    Sun, D.F.2    Toh, K.-C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.