@ARTICLE(ali-95,
AUTHOR = "F. Alizadeh",
TITLE = "Interior Point Methods in Semidefinite Programming with
Applications to Combinatorial Optimization",
JOURNAL = "{SIAM J. Optim.}",
VOLUME=5,
NUMBER=1,
PAGES="13--51",
YEAR = 1995)
@TECHREPORT(AHO-95,
AUTHOR = "F. Alizadeh and J.P Haeberly and M. Overton",
TITLE = "Complementarity and nondegeneracy in semidefinite programming",
INSTITUTION = "Rutgers Center For Operations Research",
NUMBER = "rrr46-95",
Note="To appear In {\em Math. Programming Ser. B}",
YEAR = 1995)
@UNPUBLISHED(AHO-95, AUTHOR = "F. Alizadeh and J.P Haeberly and M. Overton", TITLE = "Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results", NOTE="Submitted", YEAR = 1996)
@UNPUBLISHED(AK-94,
AUTHOR = "Noga Alon and Nabil Kahale",
TITLE="Approximating the independence number via {$\vartheta$}--function",
NOTE="{Manuscript}",
YEAR=1994)
@ARTICLE(BW-81a, AUTHOR="J. M. Borwein and H.~Wolkowicz", TITLE="Facial reduction for a cone-convex programming problem", JOURNAL="J. Austral. Math. Soc. Ser. A", VOLUME=30, PAGES="369--380", YEAR=1981)
@ARTICLE(BW-81b, AUTHOR="J. M. Borwein and H.~Wolkowicz", TITLE="Characterization of Optimality for the abstract convex program with finite dimensional range", JOURNAL="J. Austral. Math. Soc. Ser. A", VOLUME=30, PAGES="390--411", YEAR=1981)
@ARTICLE(CDW-75,
AUTHOR = "J.~Cullum and W.~E.~Donath and P.~Wolfe",
TITLE="The minimization of certain nondifferentiable sums of eigenvalue
problems",
JOURNAL = "{Math. Programming Stud.}",
VOLUME = 3,
PAGES = "35--55",
YEAR=1975)
@INPROCEEDINGS(FG-95,
AUTHOR = "Uriel Feige and Michel X. Goemans",
TITLE = "Approximating the value of two prover proof systems, with
applications to {MAX 2SAT} and {MAX DICUT}",
YEAR = 1995,
BOOKTITLE = "Proceedings of the Third Israel Symposium on
Theory of Computing and Systems")
@ARTICLE(fle-85,
AUTHOR="R.~Fletcher",
TITLE = "Semi-Definite Matrix Constraints in Optimization",
JOURNAL="{SIAM J. Control Optim.},
VOLUME=23,
PAGES="493-513",
YEAR=1985)
@TECHREPORT(fre-94,
AUTHOR = "R. M. Freund",
TITLE = "{Complexity of an Algorithm for Finding an Approximate Solution
of a Semi-Definite Program with no Regularity Assumption}",
INSTITUTION = "Operations Research Center, M.I.T.",
NUMBER = "OR-302-94",
YEAR = 1994)
@UNPUBLISHED(FJ-94,
AUTHOR= "{Alan Frieze and Mark Jerum}",
TITLE="{Improved approximation algorithms for MAX-$k$--CUT snd MAX
BISECTION}",
NOTE="{Manuscript}",
YEAR=1994)
@ARTICLE(GW-94,
AUTHOR = "Michel X. Goemans and David P. Williamson",
TITLE = "{Improved Approximation Algorithms for Maximum Cut and
Satisfiability Problems Using Semidefinite Programming}",
JOURNAL = "{J. Assoc. Comput. Mach.}",
NOTE = "{(To appear). A preliminary version appeared in Proc. 26th
Annual ACM Symposium on Theory of Computing}",
YEAR = 1994)
@UNPUBLISHED(gul-94,
AUTHOR="{Osman G{\"{u}}ler}",
TITLE="{Barrier Functions in Interior Point Methods}",
NOTE="Manuscript",
SCHOOL="University of Maryland Balitomre County",
YEAR="1994")
@book(GLS-88,
AUTHOR="M. Gr{\"{o}}tschel and L. Lov\'{a}sz and A. Schrijver",
TITLE="{Geometric Algorithms and Combinatorial Optimization}",
YEAR=1988,
PUBLISHER="Springer Verlag")
@ARTICLE(HRVW-94,
AUTHOR="C. Helmberg and F. Rendl and R. J. Vanderbei and H.
Wolkowicz",
TITLE="An Interior--Point Method for Semidefinite Programming",
JOURNAL="{SIAM J. Optim.}",
NOTE="(To appear)",
YEAR=1994)
@INPROCEEDINGS(KMS-94,
AUTHOR="David Karger and Rajeev Motwani and Madhu Sudan",
TITLE="{Improved Graph Coloring by Semidefinite Programming}",
BOOKTITLE = focs34,
YEAR=1994)
@ARTICLE(knu-95,
AUTHOR="D. E. Knuth",
TITLE="The Sandwich Theorem",
JOURNAL="{Electronic Journal of Combinatorics",
VOLUME=1,
YEAR=1995,
NOTE="Accessible via
http://ejc.math.gatech.edu:8080/Journal/Volume_1/volume1.html")
@TECHREPORT(KKH-94,
AUTHOR="M. Kojima and S. Kojima and S. Hara",
TITLE="{Linear Algebra for Semidefinite Programming",
INSTITUTION="{Department of Information Sciences, Tokyo Inst. of
Technology}",
NUMBER="{B-290}",
YEAR=1994)
@TECHREPORT(KSH-94,
AUTHOR="M. Kojima and S. Shindoh and S. Hara",
TITLE="{Interior--Point Methods for the Monotone Linear Complementarity
Problem in Symmetric Matrices}",
INSTITUTION="{Department of Information Sciences, Tokyo Inst. of
Technology}",
NUMBER="{B-282}",
YEAR=1994)
@TECHREPORT(lov-92,
AUTHOR="L.~Lov\'{a}sz ",
TITLE="{Combinatorial Optimization: Some Problems and Trends",
INSTITUTION="Center for Discrete Mathematics and Theoretical Computer
Science (DIMACS)",
NUMBER="92-53"
YEAR=1992)
@ARTICLE(LS-91,
AUTHOR="L.~Lov\'{a}sz and A.~Schrijver",
TITLE="{Cones of Matrices and Setfunctions, and 0-1 Optimization}",
JOURNAL="{SIAM J. Optim.}",
VOLUME=1,
NUMBER=2,
PAGES="166-190",
YEAR=1991)
@BOOK(NN-94,
AUTHOR = "Y.~Nesterov and A.~Nemirovskii",
TITLE="{Interior Point Polynomial Methods in Convex Programming:
Theory and Applications}",
PUBLISHER="{Society for Industrial and Applied Mathematics}",
ADDRESS="Philadelphia",
YEAR=1994)
@ARTICLE(NT-94,
AUTHOR="{Nesterov, Yu. E. and Todd, Michael J.}",
TITLE="{Self-Scaled Cones and Interior--Point Methods in Nonlinear
Programming}",
JOURNAL="{Mathematics of Operations Research"},
NOTE="{submitted}",
MONTH="April",
YEAR=1994)
@ARTICLE(NT-95,
AUTHOR="{Nesterov, Yu. E. and Todd, Michael J.}",
TITLE="{Primal_dual Interior Point methods for Self-Scaled Cones"},
JOURNAL="{SIAM J. on Optimization}",
NOTE="{To appear}",
YEAR=1995)
@ARTICLE(ove-88,
AUTHOR="M.~L. Overton",
TITLE="On minimizing the Maximum Eigenvalue of a Symmetric Matrix",
JOURNAL="{SIAM J. Matrix Anal. Appl.}",
VOLUME=9,
NUMBER=2,
PAGES="256-268",
YEAR=1988)
@ARTICLE(OW-91a,
AUTHOR="M.~L. Overton and R.~S. Womersley",
TITLE="Optimality Conditions and Duality Theory for Minimizing sums of
the Largest Eigenvalues of Symmetric Matrices",
JOURNAL="{Math. Programming}",
VOLUME=62,
NUMBER=2,
PAGES="321-357",
YEAR=1993)
@ARTICLE(OW-91b,
AUTHOR="M.~L. Overton and R.~S. Womersley",
TITLE="On the Sum of the Largest Eigenvalues of a Symmetric Matrix",
JOURNAL="{SIAM J. Matrix Anal. Appl.}",
VOLUME=13,
PAGES="41-45",
YEAR=1992)
@TECHREPORT(pat-94,
AUTHOR="G. Pataki",
TITLE="On the Multiplicity of optimal eigenvalues",
INSTITUTION="{Graduate School of Industrial Administration, Garnegie--Mellon
University}",
NUMBER="{MSRR-604}",
YEAR=1994)
@PHDTHESIS(ram-93, AUTHOR = "Motakuri Venkata Ramana", TITLE="An Algorithmic Analysis of Multiquadratic and Semidefinite Programming Problems", SCHOOL = "Johns Hopkins University", YEAR = 1993)
@TECHREPORT(ram-95,
AUTHOR = "Motakuri Venkata Ramana",
TITLE="An Exact duality Theory for Semidefinite Programming and its
Complexity Implications",
INSTITUTION="DIMACS",
NUMBER="{95-02}",
YEAR = 1995)
@TECHREPORT=VB-94, AUTHOR = "Lieven Vandenberghe and Stephen Boyd", TITLE = "Semidefinite Programming", INSTITUTION="Information Systems Laboratory, Stanford University", YEAR=1994)
@TECHREPORT(VB-93,
AUTHOR = "L. Vandenberghe and S. Boyd ",
TITLE = "Primal--dual potential reduction method for problems involving
matrix inequalities",
INSTITUTION = "{Information Systems Laboratory, Department of Electrical
Engineering, Stanford University, Stanford, CA}",
YEAR = "1993",
NOTE="{\em Math. Prog.} (to appear)",
MONTH = "January")
@ARTICLE(wol-81,
AUTHOR="H.~Wolkowicz",
TITLE = "Some applications of optimization in matrix theory",
JOURNAL="{Linear Algebra Appl.}",
VOLUME=40,
PAGES="101--118",
YEAR=1981)