@incollection{Beale, author = "E. M. L. Beale", title = "A derivation of conjugate gradients", booktitle = "Numerical Methods for Nonlinear Optimization", publisher = "Academic Press", year = "1972", pages = "39--43", editor = "F. A. Lootsma", address = "London, England", } @techreport{BendsoeBZ, author = "M. P. Bends{\o}e and A. Ben-Tal and J. Zowe", title = "Optimization Methods for Truss Geometry and Topology Design", institution = "Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion", address = "Haifa, Israel", type = "Research Report", number = "3/93", year = "1993" } @techreport{Ben-TalYZ, author = "A. Ben-Tal and I. Yuzefovich and M. Zibulevsky", title = "Penalty/Barrier Multiplier Methods for Minimax and Constrained Smooth Convex Problems", institution = "Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion", address = "Haifa, Israel", type = "Research Report", number = "9/92", year = "1992" } @techreport{Ben-TalZ, author = "A. Ben-Tal and M. Zibulevsky", title = "Penalty/Barrier Multiplier Methods for Large-Scale Convex Programming Problems", institution = "Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion", address = "Haifa, Israel", type = "Research Report", number = "6/93", year = "1993" } @book{Bertsekas, author = "D. P. Bertsekas", title = "Constrained Optimization and {L}agrange Multiplier Methods", publisher = "Academic Press", address = "London, New York", year = "1982" } @techreport{BongartzCGT, author = "I. Bongartz and A. R. Conn and N. I. M. Gould and Ph. L. Toint", title = "{CUTE: Constrained and Unconstrained Testing Environment}", type = "Technical Report", number = "93/10", year = "1993", institution = "Department of Mathematics, Facult\'e Universitaires de Namur", address = "Namur, Belgium" } @inproceedings{BreitfeldS1, author = "M. G. Breitfeld and D. F. Shanno", title = "Preliminary Computational Experience with Modified Log-Barrier Functions for Large-Scale Nonlinear Programming", booktitle = "Large Scale Optimization: State of the Art", year = "1994", pages = "45 -- 67", editor = "W. W. Hager and D. W. Hearn and P. M. Pardalos", publisher = "Kluwer Academic Publishers B.V." } @techreport{BreitfeldS2, author = "M. G. Breitfeld and D. F. Shanno", title = "Computational Experience with Penalty-Barrier Methods for Nonlinear Programming", type = "RUTCOR Research Report", number = "RRR 17-93 (revised March 1994)", year = "1993", institution = "Rutgers Center for Operations Research, Rutgers University", address = "New Brunswick, New Jersey", note = "{S}ubmitted to {\em Annals of Operations Research}" } @techreport{BreitfeldS3, author = "M. G. Breitfeld and D. F. Shanno", title = "A Globally Convergent Penalty-Barrier Algorithm for Nonlinear Programming and its Computational Performance", type = "RUTCOR Research Report", number = "RRR 12-94", year = "1994", institution = "Rutgers Center for Operations Research, Rutgers University", address = "New Brunswick, New Jersey", note = "{S}ubmitted to {\em Mathematical Programming}" } @article{Carroll, author = "C. W. Carroll", title = "The Created Response Surface Technique for Optimizing Nonlinear Restrained Systems", journal = "Operations Research", volume = "9", year = "1961", pages = "169--184" } @incollection{ConcusGO, author = "P. Concus and G. Golub and D. P. O'Leary", title = "A generalized conjugate-gradient method for the numerical solution of elliptic partial differential equations", booktitle = "Sparse Matrix Computations", year = "1976", pages = "309--332", editor = "J. Bunch and D. Rose", publisher = "Academic Press", address = "New York" } @article{ConnGT1, author = "A. R. Conn and N. I. M. Gould and Ph. L. Toint", title = "A globally convergent augmented {L}agrangian algorithm for optimization with general constraints and simple bounds", journal = "SIAM Journal on Numerical Analysis", volume = "28", number = "2", year = "1991", pages = "545--572" } @techreport{ConnGT2, author = "A. R. Conn and N. I. M. Gould and Ph. L. Toint", title = "A globally convergent {L}agrangian barrier algorithm for optimization with general inequality constraints and simple bounds", type = "Technical Report", number = "92/07", year = "1992", institution = "Department of Mathematics, Facult\'e Universitaires de Namur", address = "Namur, Belgium" } @book{ConnGT3, author = "A. R. Conn and N. I. M. Gould and Ph. L. Toint", title = "{LANCELOT}: a {F}ortran package for large-scale nonlinear optimization ({R}elease {A})", publisher = "Springer-Verlag", year = "1992", address = "Heidelberg, Berlin, New York", series = "{S}pringer Series in Computational Mathematics", number = "17" } @techreport{ConnGT4, author = "A. R. Conn and N. I. M. Gould and Ph. L. Toint", title = "Numerical Experiments with the {LANCELOT} Package ({R}elease {A}) for Large-Scale Nonlinear Optimization", type = "Technical Report", number = "92/16(revised)", year = "1992", institution = "Department of Mathematics, Facult\'e Universitaires de Namur", address = "Namur, Belgium" } @article{Dembo, author = "R. S. Dembo", title = "A set of geometric programming test problems and their solutions", journal = "Mathematical Programming", volume = "10", year = "1976", pages = "192--213" } @article{DemboS, author = "R. S. Dembo and T. Steihaug", title = "Truncated-{N}ewton algorithms for large-scale unconstrained optimization", journal = "Mathematical Programming", volume = "26", year = "1983", pages = "190--212" } @book{DennisS, author = "J. E. Dennis and R. B. Schnabel", title = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", publisher = "Prentice-Hall", series = "Prentice-Hall Series in Computational Mathematics", address = "Englewood Cliffs, New Jersey", year = "1983" } @techreport{El-BakryTTZ, author = "A. S. El-Bakry and R. A. Tapia and T Tsuchiya and Y. Zhang", title = "On the Formulation and Theory of the Primal-Dual Newton Interior-Point Method for Nonlinear Programming", type = "Technical Report", number = "TR92-40", year = "December 1992 (revised October 1993)", institution = "Department of Computational and Applied Mathematics, Rice University", address = "Houston, Texas" } @book{FiaccoMcC, author = "A. V. Fiacco and G. P. McCormick", title = "Nonlinear Programming: Sequential Unconstrained Minimization Techniques", publisher = "John Wiley \& Sons", year = "1968", address = "New York", note = "Reprint: Volume 4 of {\em SIAM Classics in Applied Mathematics}, SIAM Publications, Philadelphia, Pennsylvania, 1990" } @book{Fletcher, author = "R. Fletcher", title = "Practical Methods of Optimization", publisher = "John Wiley~\&~Sons", address = "New York", edition = "second", year = "1987" } @book{FloudasP, author = "C. A. Floudas and P. M. Pardalos", title = "A Collection of Test Problems for Constrained Global Optimization Algorithms", publisher = "Springer-Verlag", year = "1990", address = "Berlin", series = "Lecture Notes in Computer Science", volume = "455" } @techreport{Frisch, author = "K. R. Frisch", title = "The logarithmic potential method for convex programming", type = "Unpublished manuscript", year = "1955", month = "May", institution = "Institute of Economics, University of Oslo", address = "Oslo, Norway" } @techreport{GillM1, author = "P. E. Gill and W. Murray", title = "Safeguarded Steplength Algorithms for Optimization Using Descent Methods", institution = "National Physical Laboratory", address = "Teddington, England", year = "1974", type = "Report", number = "NAC 37" } @article{GillM2, author = "P. E. Gill and W. Murray", title = "Newton-type Methods for Unconstrained and Linearly Constrained Optimization", journal = "Mathematical Programming", volume = "7", year = "1974", pages = "311--350" } @book{GillMW, author = "P. E. Gill and W. Murray and M. H. Wright", title = "Practical Optimization", publisher = "Academic Press", address = "London", year = "1981" } @article{Hestenes, author = "M. R. Hestenes", title = "Multiplier and Gradient Methods", journal = "Journal of Optimization Theory and Applications", volume = "4", year = "1969", pages = "303--320" } @book{HockS, author = "W. Hock and K. Schittkowski", title = "Test Examples for Nonlinear Programming Codes", publisher = "Springer-Verlag", year = "1981", address = "Berlin", series = "Lecture Notes in Economics and Mathematical Systems", number = "187" } @techreport{IusemST, author = "A. N. Iusem and B. F. Svaiter and M. Teboulle", title = "Entropy-Like Proximal Methods in Convex Programming", institution = "Department of Mathematics and Statistics, University of Maryland", address = "Baltimore, Maryland", year = "May 1992 (revised May 1993)", type = "Research Report" } @techreport{JensenP, author = "D. L. Jensen and R. Polyak", title = "The Convergence of a Modified Barrier Method for Convex Programming", institution = "IBM Research Division, T. J. Watson Research Center", address = "Yorktown Heights, New York", year = "1992", type = "Research Report", number = "RC 18570" } @techreport{JensenPS, author = "D. L. Jensen and R. Polyak and R. Schneur", title = "Numerical Experience with Modified Barrier Functions for Linear Programming", institution = "IBM Research Division, T. J. Watson Research Center", address = "Yorktown Heights, New York", year = "1992", type = "Research Report", number = "RC 18415" } @article{JittorntrumO, author = "K. Jittorntrum and M. Osborne", title = "A modified barrier function method with improved rate of convergence for degenerate problems", journal = "Journal of the Australian Mathematical Society (Series B)", volume = "21", year = "1980", pages = "305--329" } @article{LiuN, author = "D. C. Liu and J. Nocedal", title = "On the Limited Memory {BFGS} Method for Large Scale Optimization", journal = "Mathematical Programming", volume = "45", year = "1989", pages = "503--528" } @book{McCormick, author = "G. P. McCormick", title = "Nonlinear Programming", publisher = "John Wiley \& Sons", year = "1983", address = "New York" } @article{McCormick1, author = "G. P. McCormick", title = "The projective {SUMT} method for convex optimization", journal = "Mathematics of Operations Research", volume = "14", year = "1989", pages = "203--224" } @incollection{MoreS, author = "J. J. Mor\'{e} and D. C. Sorensen", title = "Newton's Method", booktitle = "Studies in Numerical Analysis", publisher = "Mathematical Association of America", year = "1984", pages = "29--82", editor = "G. A. Golub" } @techreport{MoreT, author = "J. J. Mor\'{e} and D. J. Thuente", title = "Line Search Algorithms with Guaranteed Sufficient Decrease", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", address = "Argonne. Illinois", year = "1992", type = "Preprint", number = "MCS-P330-1092" } @article{Murray, author = "W. Murray", title = "Analytical expressions for eigenvalues and eigenvectors of the {H}essian matrices of barrier and penalty functions", journal = "Journal of Optimization Theory and Applications", volume = "7", year = "1971", pages = "181--196" } @article{MurrayW, author = "W. Murray and M. H. Wright", title = "Line search procedures for the logarithmic barrier function", journal = "SIAM Journal on Optimization", volume = "4", number = "2", year = "1994", pages = "229--246" } @article{Nash, author = "S. G. Nash", title = "Preconditioning of Truncated-{N}ewton Methods", journal = "SIAM Journal of Science and Statistical Computations", volume = "6", year = "1985", pages = "599--616" } @article{NashN, author = "S. G. Nash and J. Nocedal", title = "A Numerical Study of the Limited Memory {BFGS} Method and the Truncated-{N}ewton Method for Large Scale Optimization", journal = "SIAM Journal of Optimization", volume = "1", number = "3", year = "1991", pages = "358--372" } @inproceedings{NashPS, author = "S. G. Nash and R. Polyak and A. Sofer", title = "A Numerical Comparison of Barrier and Modified-Barrier Methods for Large-Scale Bound-Constrained Optimization", booktitle = "Large Scale Optimization: State of the Art", year = "1994", pages = "319 -- 338", editor = "W. W. Hager and D. W. Hearn and P. M. Pardalos", publisher = "Kluwer Academic Publishers B.V." } @article{NashS, author = "S. G. Nash and A. Sofer", title = "A Barrier Method for Large-Scale Constrained Optimization", journal = "ORSA Journal on Computing", volume = "5", year = "1993", pages = "40--53" } @unpublished{NashSS, author = "S. G. Nash and A. Sofer and M. Srinivasan", title = "Using Directions of Negative Curvature in Truncated-{N}ewton Methods", note = "{P}resented at the ORSA/TIMS National Meeting, Phoenix, AZ, 1993", } @article{Nocedal, author = "J. Nocedal", title = "Updating Quasi-{N}ewton Matrices with Limited Storage", journal = "Mathematics of Computation", volume = "35", year = "1980", pages = "773--782" } @article{Polyak, author = "R. Polyak", title = "Modified barrier functions (theory and methods)", journal = "Mathematical Programming", volume = "54", year = "1992", pages = "177--222" } @incollection{Powell, author = "M. J. D. Powell", title = "A Method for Nonlinear Constraints in Minimization Problems", booktitle = "Optimization", year = "1969", editor = "R. Fletcher", publisher = "Academic Press", address = "London, New York" } @article{Shanno1, author = "D. F. Shanno", title = "Conditioning of Quasi-{N}ewton Methods for Function Minimization", journal = "Mathematics of Computation", volume = "24", year = "1970", pages = "647--656" } @article{Shanno, author = "D. F. Shanno", title = "Conjugate Gradient Methods with Inexact Searches", journal = "Mathematics of Operations Research", volume = "3", year = "1978", pages = "244--256" } @article{ShannoP, author = "D. F. Shanno and K. H. Phua", title = "Numerical Experience with Sequential Quadratic Programming Algorithms for Equality Constrained Nonlinear Programming", journal = "Transactions on Mathematical Software", volume = "15", number = "1", year = "1989", pages = "49--63" } @article{ShannoP2, author = "D. F. Shanno and K. H. Phua", title = "Remark on algorithm 500. {M}inimization of unconstrained multivariate functions", journal = "Transactions on Mathematical Software", volume = "6", year = "1980", pages = "618--622" } @book{StoerB, author = "J. Stoer and R. Bulirsch", title = "Introduction to Numerical Analysis", publisher = "Springer-Verlag", year = "1993", edition = "second", address = "New York", series = "Texts in Applied Mathematics", number = "12" } @incollection{Wright, author = "M. H. Wright", title = "Interior Methods for Constrained Optimization", booktitle = "Acta Numerica", editor = "A. Iserles", publisher = "Cambridge University Press", address = "New York", year = "1992", pages = "341--407" } @techreport{Wright2, author = "M. H. Wright", title = "Determining Subspace Information from the {H}essian of the barrier function", type = "{Numerical Analysis Manuscript}", number = "92--02", year = "1992", institution = "AT\&T Bell Laboratories", address = "Murray Hill, New Jersey" }