Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming

[1]  D. Rose Triangulated graphs and the elimination process , 1970 .

[2]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[3]  H. Dym,et al.  Extensions of band matrices with band inverses , 1981 .

[4]  S. M. Robinson Local structure of feasible sets in nonlinear programming , 1983 .

[5]  S. M. Robinson Local Structure of Feasible Sets in Nonlinear Programming - Part II. Nondegeneracy , 1984 .

[6]  Charles R. Johnson,et al.  Positive definite completions of partial Hermitian matrices , 1984 .

[7]  C. Richard Johnson,et al.  Matrix Completion Problems: A Survey , 1990 .

[8]  W. Barrett,et al.  The real positive definite completion problem for a 4-cycle , 1993 .

[9]  M. Laurent The real positive semidefinite completion problem for series-parallel graphs , 1997 .

[10]  Charles R. Johnson,et al.  The Real Positive Definite Completion Problem: Cycle Completability , 1996 .

[11]  Michael L. Overton,et al.  Complementarity and nondegeneracy in semidefinite programming , 1997, Math. Program..

[12]  Henry Wolkowicz,et al.  An Interior-Point Method for Approximate Positive Semidefinite Completions , 1998, Comput. Optim. Appl..

[13]  M. Laurent A connection between positive semidefinite and euclidean distance matrix completion problems , 1998 .

[14]  Charles R. Johnson,et al.  Critical Graphs for the Positive Definite Completion Problem , 1998, SIAM J. Matrix Anal. Appl..

[15]  Charles R. Johnson,et al.  Positive definite completions and determinant maximization , 1999 .

[16]  H. Wolkowicz,et al.  Matrix Completion Problems , 2000 .

[17]  J. Frédéric Bonnans,et al.  Perturbation Analysis of Optimization Problems , 2000, Springer Series in Operations Research.

[18]  Henry Wolkowicz,et al.  Semidefinite programming for discrete optimization and matrix completion problems , 2002, Discret. Appl. Math..

[19]  N. Higham Computing the nearest correlation matrix—a problem from finance , 2002 .

[20]  K. J. Harrison,et al.  Matrix Completions and Chordal Graphs , 2003 .

[21]  Nicos Christofides,et al.  Correlation stress testing for value-at-risk , 2003 .

[22]  M. Todd,et al.  Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems , 2005 .

[23]  Defeng Sun,et al.  A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix , 2006, SIAM J. Matrix Anal. Appl..

[24]  Defeng Sun,et al.  The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications , 2006, Math. Oper. Res..

[25]  Inderjit S. Dhillon,et al.  Matrix Nearness Problems with Bregman Divergences , 2007, SIAM J. Matrix Anal. Appl..

[26]  Kim-Chuan Toh,et al.  An inexact primal–dual path following algorithm for convex quadratic SDP , 2007, Math. Program..

[27]  Defeng Sun,et al.  Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming , 2008, SIAM J. Optim..

[28]  Monique Laurent,et al.  Matrix Completion Problems , 2009, Encyclopedia of Optimization.

[29]  Houduo Qi,et al.  Local Duality of Nonlinear Semidefinite Programming , 2009, Math. Oper. Res..