ref-baire.bib

%  BibFile containing references in optimization and
%  related topics.
%
%  The format of the of the BibTex entry label is :
%
%     <Lastname_morenames_YearLetter> .
%
%  For example, the key from a book by Dennis and Schnabel is :
%
%     Dennis_Schnabel_1983 .
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  The following are string macros for the standard journal
%  abbreviations used in the review journal Mathematical Reviews.
%
@string{annals = "Ann. of Math."}
@string{astat = "Ann. Math. Statist."}
@string{actan = "Acta Numer."}
@string{amj = "Amer. J. Math."}
@string{amc = "Appl. Math. Comput."}
@string{bit = "BIT"}
@string{cacm = "Commun. ACM"}
@string{coap = "Comput. Optim. Appl."}
@string{ejor = "European J. Oper. Res."}
@string{etna = "Electron. Trans. Numer. Anal."}
@string{fcm = "Found. Comput. Math."}
@string{imana = "IMA J. Numer. Anal."}
@string{itmtt = "IEEE Trans. Microw. Theory Tech."}
@string{jcomam = "J. Comput. Appl. Math."}
@string{jcp = "J. Comput. Phys."} 
@string{jogo = "J. Global Optim."}
@string{jota = "J. Optim. Theory Appl."}
@string{jrssb = "J. R. Stat. Soc. Ser. B. Stat. Methodol."}
@string{jmaa = "J. Math. Anal. Appl."}
@string{mathcomput = "Math. Comp."}
@string{mprog = "Math. Program."}
@string{mprogc = "Math. Program. Comput."}
@string{nmath = "Numer. Math."}
@string{nlaa = "Numer. Linear Algebra Appl."}
@string{operres = "Oper. Res."}
@string{opteng = "Optim. Eng."}
@string{optl = "Optim. Lett."}
@string{optms = "Optim. Methods Softw."}
@string{qam = "Quart. Appl. Math."}
@string{qor = "4OR"}
@string{sico = "SIAM J. Control Optim."}
@string{siis = "SIAM J. Imaging Sci."}
@string{sinum = "SIAM J. Numer. Anal. "}
@string{siopt = "SIAM J. Optim."}
@string{sirev = "SIAM Rev."}
@string{sisc = "SIAM J. Sci. Comput."}
@string{sistc = "SIAM J. Sci. Stat. Comp."}
@string{simax = "SIAM J. Matrix Anal. Appl."}
@string{tams = "Trans. Amer. Math. Soc."}
@string{toms = "ACM Trans. Math. Software"}

%  The following are string macros for the standard series 
%  abbreviations used in the review journal Mathematical Reviews.
@string{asoc = "Athena Sci. Optim. Comput. Ser."}
@string{cse = "Comput. Sci. Eng."}
@string{mpso = "MPS-SIAM Ser. Optim."}
@string{moso = "MOS-SIAM Ser. Optim."}
@string{pms = "Princeton Math. Ser."}
@string{sscm = "Springer Ser. Comput. Math."}
@string{scam = "Ser. Contemp. Appl. Math. CAM"}
@string{soa = "Springer Optim. Appl."}
@string{sorfe = "Springer Ser. Oper. Res. Financ. Eng."}
@string{aopt = "Appl. Optim."}
@string{gmw = "Grundlehren Math. Wiss."}
@string{fam = "Frontiers Appl. Math."}
@string{lncse = "Lect. Notes Comput. Sci. Eng."}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@article{Levenberg_1944,
title = {A method for the solution of certain non-linear problems in least squares},
author = {Levenberg, K.},
journal = qam,
volume = {2},
pages = {164--168},
year = {1944}
}

@article{Marquardt_1963,
title = {An algorithm for least-squares estimation of nonlinear parameters},
author = {Marquardt, D. W.},
journal = {J. Soc. Indust. Appl. Math.} ,
volume = {11},
pages = {431--441},
year = {1963},
}

@article{Armijo_1966,
author = {Armijo, L.},
journal = {Pacific J. Math.},
pages = {1--3},
title = {Minimization of functions having {L}ipschitz continuous first partial derivatives},
volume = {16},
year = {1966}
}

@article{Osborne_1976, 
title = {Nonlinear least squares --- the {Levenberg} algorithm revisited}, 
volume = {19}, 
journal = {J. Austral. Math. Soc.},
author = {Osborne, M. R.}, 
year = {1976}, 
pages = {343–357}
}

@article{Rockafellar_1976,
title = {Monotone operators and the proximal point algorithm},
author = {Rockafellar, R. T.},
journal = sico,
volume = {14},
pages = {877--898},
year = {1976},
}

@article{Parikh_Boyd_2014,
title = {Proximal algorithms},
author = {Parikh, N. and Boyd, S.},
journal = {Found. Trends Optim.},
volume = {1},
pages = {127--239},
year = {2014},
}

@article{Bramble_Pasciak_Schatz_1986, 
author = {Bramble,  J. and Pasciak, J.  and Schatz, A.}, 
title = {The construction of preconditioners for elliptic problems by substructuring, {I}},
journal = mathcomput,
year = {1986},
volume = {47},
pages = {103--134}
}

@article{GBDantzig_PWolfe_1960,
title = {Decomposition principle for linear programs},
author = {G. B. Dantzig and P. Wolfe},
journal = operres,
volume = {8},
pages = {101--111},
year = {1960},
publisher = {INFORMS}
}

@incollection{Powell_1975,
title = {Convergence properties of a class of minimization algorithms},
author = {Powell, M. J. D.},  
editor = {Mangasarian, O. L. and Meyer, R. R. and Robinson, S. M.},
booktitle = {Nonlinear Programming 2: Proceedings of the
Special Interest Group on Mathematical Programming
Symposium Conducted by the Computer Sciences
Department at the University of Wisconsin-Madison,
April 15--17, 1974},
pages = {1--27},
year = {1975},
publisher = {Academic Press}
}

@article{Powell_1984,
author = {Powell, M. J. D.},
title = {On the global convergence of trust region algorithms for unconstrained minimization},
journal = mprog,
volume = {29},
pages = {297-303},
year = {1984},
}

@article{Xu_1992,
title = {Iterative methods by space decomposition and subspace correction},
author = {Xu, J.},
journal = sirev,
volume = {34},
pages = {581--613},
year = {1992}
}

@article{MCFerris_OLMangasarian_1994,
author = {M. C. Ferris and O. L. Mangasarian},
title = {Parallel variable distribution},
journal = siopt,
volume = {4}, 
pages = {815--832},
year = {1994}
}

@article{Mangasarian_1995,
title = {Parallel gradient distribution in unconstrained optimization},
author = {Mangasarian, O. L.},
journal = sico,
volume = {33},
pages = {1916--1925},
year = {1995},
}

@incollection{ARConn_NGould_ASartenaer_PhLToint_1994,
author = {A. R. Conn and N. Gould and A. Sartenaer and Ph. L. Toint}, 
title = {On iterated-subspace minimization methods for nonlinear
optimization},
booktitle = {Linear and nonlinear conjugate gradient-related methods},
editor = {L. M. Adams and J. L. Nazareth},
pages = {50--78},
year = {1994},
publisher = {SIAM},
address = {Philadelphia}
}

@article{MGriebel_POswald_1995,
title = {On the abstract theory of additive and multiplicative {Schwarz} algorithms},
author = {M. Griebel and P. Oswald},
journal = nmath,
volume = {70},
pages = {163--180},
year = {1995},
publisher = {Springer}
}

@article{SolodovMV_ZavrievSK_1998,
title = {Error stability properties of generalized gradient-type algorithms},
author = {Solodov, M. V. and Zavriev, S. K.},
journal = jota,
volume = {98},
pages = {663--680},
year = {1998},
}
@article{Solodov_1997,
author = {M. V. Solodov}, 
title = {New inexact parallel variable distribution algorithms},
journal = coap,
volume = {7},
pages = {165-182},
year = {1997}
}

@techreport{JEDennis_TSteihaug_1998,
title = {A {Ferris-Mangasarian} Technique Applied to Linear Least
Squares Problems},
author = {J. E. {Dennis, Jr.} and T. Steihaug},
year = {1998},
institution = {Center for Research on Parallel Computation, Rice
University},
number = {CRPC-TR98740}
}

@article{Fukushima_1998,
author = {M. Fukushima}, 
title = {Parallel variable transformation in unconstrained optimization},
journal = siopt,
volume = {8}, 
year = {1998},
pages = {658--672}
}

@book{DPBertsekas_1999,
title = {Nonlinear Programming},
author = {D. P. Bertsekas},
year = {1999},
edition = {Second},
series = asoc,
volume = {4},
publisher = {Athena Scientific},
address = {Massachusetts}
}

@article{Cai_Sarkis_1999,
title = {A restricted additive {Schwarz} preconditioner for general sparse linear systems},
author = {Cai, X.-C. and Sarkis, M.},
journal = sisc,
volume = {21},
pages = {792--797},
year = {1999},
publisher = {SIAM}
}

@article{Frommer_Renaut_1999,
author = {Frommer, A. and Renaut, R. A.},
title = {A unified approach to parallel space decomposition methods},
journal = jcomam,
volume = {110},
pages = {205--223},
year = {1999},
}

@article{Tai_Xu_2002,
title = {Global and uniform convergence of subspace correction methods for some convex optimization problems},
author = {Tai, X.-C. and Xu, J.},
journal = mathcomput,
volume = {71},
pages = {105--124},
year = {2002}
}

@article{Cai_Keyes_2002,
title = {Nonlinearly preconditioned inexact {Newton} algorithms},
author = {Cai, X.-C. and Keyes, D. E.},
journal = sisc,
volume = {24},
pages = {183--200},
year = {2002},
publisher = {SIAM}
}

@book{Saad_2003,
title = {Iterative Methods for Sparse Linear Systems},
author = {Y. Saad},
year = {2003},
edition = {Second},
publisher = {SIAM},
address = {Philadelphia}
}

@incollection{Yuan_2007,
author = {Y. Yuan},
title = {Subspace techniques for nonlinear optimization},
booktitle = {Some topics in industrial and applied mathematics},
editor = {R. Jeltsch and T.-T. Li and I. H. Sloan},
pages = {206--218},
year = {2007},
publisher = {World Scientific Publishing},
address = {Singapore}
}

@incollection{Yuan_2014,
author = {Yuan, Y.},
title = {A review on subspace methods for nonlinear optimization},
booktitle = {Proceedings of the International Congress of Mathematicians (Seoul 2014)},
editor = {Jang, S. Y. and Kim, Y. R. and Lee D.-W. and Yie, I.},
pages = {807--827},
year = {2014},
publisher = {Kyung Moon Sa Co. Ltd.},
address = {Seoul}
}

@article{Ni_Yuan_1997,
title = {A subspace limited memory quasi-{N}ewton algorithm for large-scale nonlinear bound constrained optimization},
author = {Ni, Q. and Yuan, Y.},
journal = mathcomput,
volume = {66},
pages = {1509--1520},
year = {1997}
}
@article{Wang_Yuan_2006,
title = {A subspace implementation of quasi-{Newton} trust region methods for unconstrained optimization},
author = {Wang, Z. and Yuan, Y.},
journal = nmath,
volume = {104},
pages = {241--269},
year = {2006},
}

@misc{SBoyd_LXiao_AMutapcic_JMattingley_2008,
author = {S. Boyd and L. Xiao and A. Mutapcic and J. Mattingley},
title = {Notes on Decomposition Methods},
howpublished = {Notes for EE364B, Stanford University},
year = {2008},
}

@article{CAudet_JEDennis_SLeDigabel_2008,
author = {C. Audet and J. E. {Dennis, Jr.} and S. Le Digabel},
title = {Parallel space decomposition of the mesh adaptive direct search algorithm},
journal = siopt,
volume = {19}, 
year = {2008},
pages = {1150--1170}
}

@article{YYuan_2009,
author = {Y. Yuan},
title = {Subspace methods for large scale nonlinear equations and nonlinear least squares},
journal = opteng,
year = {2009},
volume = {10},
pages = {207--218},
publisher = {Springer},
}

@phdthesis{Sharapov_1997,
title = {Multilevel Subspace Correction for Large-Scale Optimization
Problems},
author = {Sharapov, I. A.},
year = {1997},
school = {University of California},
address = {California}
}

@book{Nocedal_Wright_2006,
title = {Numerical Optimization},
author = {Nocedal, J. and Wright, S.},
edition = {Second},
series = sorfe,
publisher = {Springer},
address = {New York},
year = {2006}
}

@book{Bertsekas_1999,
author = {Bertsekas, D. P.},
publisher = {Athena Scientific},
title = {Nonlinear Programming},
year = {1999}
}

@book{Conn_Gould_Toint_2000,
title = {Trust-Region Methods},
author = {Conn, A. R. and Gould, N. I. M. and Toint, Ph. L.},
year = {2000},
publisher = {SIAM},
address = {Philadelphia}
}

@article{Grapiglia_Yuan_Yuan_2015,
title = {On the convergence and worst-case complexity of
trust-region and regularization methods for unconstrained
optimization},
author = {Grapiglia, G. N. and Yuan, J. and Yuan, Y.},
journal = mprog,
pages = {491--520},
volume = {152},
year = {2015},
}

@article{Gratton_Sartenaer_Toint_2008,
title = {Recursive trust-region methods for multiscale nonlinear optimization},
author = {Gratton, S. and Sartenaer, A. and Toint, Ph. L.},
journal = siopt,
volume = {19},
pages = {414--444},
year = {2008},
}

@article{Gross_Krause_2009,
author = {Gro{\ss}, C. and Krause, R.},
title = {On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear
Mechanics},
journal = siopt,
volume = {47},
pages = {3044-3069},
year = {2009},
}

@article{Nash_2000,
title = {A multigrid approach to discretized optimization problems},
author = {Nash, S. G.},
journal = optms,
volume = {14},
pages = {99--116},
year = {2000},
}

@article{Lewis_Nash_2005,
title = {Model problems for the multigrid optimization of systems governed by differential equations},
author = {Lewis, R. M. and Nash, S. G.},
journal = sisc, 
volume = {26},
pages = {1811--1837},
year = {2005},
}

@article{Yuan_2009,
title = {Subspace methods for large scale nonlinear equations and nonlinear least squares},
author = {Yuan, Y.},
journal = opteng,
volume = {10},
pages = {207--218},
year = {2009},
}

@article{Toint_1988,
title = {Global Convergence of a Class of Trust-Region Methods for Nonconvex Minimization in {Hilbert} Space},
author = {Toint, {Ph. L.}},
journal = imana,
volume = {8},
pages = {231--252},
year = {1988},
}

@article{Carter_1993,
title = {Numerical experience with a class of algorithms for
nonlinear optimization using inexact function and gradient
information},
author = {Carter, R. G.},
journal = sisc,
volume = {14},
year = {1993},
}

@article{Carter_1991a,
title = {On the global convergence of trust region algorithms using inexact gradient information},
author = {Carter, R. G.},
journal = sinum,
volume = {28},
pages = {251--265},
year = {1991},
}

@incollection{More_1983,
title = {Recent developments in algorithms and software for trust region methods},
author = {Mor{\'e}, J. J.},
booktitle = {Mathematical Programming: The State of Art},
editor = {Bachem, A. and Gr\"otschel, M. and Korte, B.},
year = {1983},
publisher = {Springer-Verlag},
address = {Berlin}
}

@techreport{Carter_1991b,
title = {A Worst-case Example Using Linesearch Methods for Numerical
Optimization with Inexact Gradient Evaluations},
author = {Carter, R. G.},
institution = {Argonne National Laboratory},
number = {MCS-P283-1291},
year = {1991}
}

@article{Frommer_Schwandt_1997,
title = {A unified representation and theory of algebraic additive
{Schwarz} and multisplitting methods},
author = {Frommer, A. and Schwandt, H.},
journal = simax,
volume = {18},
pages = {893--912},
year = {1997}
}

@article{Frommer_Szyld_1999,
title = {Weighted max norms, splittings, and overlapping additive {Schwarz} iterations},
author = {Frommer, A. and Szyld, D. B.},
journal = nmath,
volume = {83},
pages = {259--278},
year = {1999},
}

@article{Frommer_Szyld_2002,
title = {An Algebraic Convergence Theory for Restricted Additive
{Schwarz} Methods Using Weighted Max Norms},
author = {Frommer, A. and Szyld, D. B.},
journal = sinum,
volume = {39},
pages = {463-479},
year = {2002}
}

@article{Polyak_1964,
title = {Some methods of speeding up the convergence of iteration methods},
author = {Polyak, B. T.},
journal = {USSR Computational Mathematics and Mathematical Physics},
volume = {4},
pages = {1--17},
year = {1964},
}

@article{Nesterov_2012,
author = {Nesterov, Yu.},
title = {Efficiency of coordinate descent methods on huge-scale optimization problems},
journal = siopt,
volume = {22},
pages = {341-362},
year = {20112}
}

@article{Nesterov_1983,
title = {A method of solving a convex programming problem with
$\mathcal{O}(1/k^2)$ convergence rate},
author = {Nesterov, Yu.},
journal = {Soviet Mathematics Doklady}, 
year = {1983},
volume = {27},
pages = {372-376}
}
@book{Nesterov_2004,
title = {Introductory Lectures on Convex Optimization: A Basic
Course},
author = {Yu. Nesterov},
year = {2004},
publisher = {Kluwer Academic Publishers},
address = {London},
}

@incollection{Cartis_Gould_Toint_2019,
title = {Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled {KKT} conditions and high-order models},
author = {Cartis, C. and Gould, N. I. M. and Toint, Ph. L.},
year = {2019},
booktitle = {Approximation and Optimization},
editor = {Demetriou, I. C. and Pardalos, P. M.},
address = {Berlin},
publisher = {Springer}
}

@techreport{Cartis_Gould_Toint_2015_b,
title = {Improved worst-case evaluation complexity for potentially
rank-deficient nonlinear least-{Euclidian}-norm problems using higher-order regularized models},
author = {Cartis, C. and Gould, N. I. M. and Toint, Ph. L.},
year = {2015},
number = {NAXYS-12-2015},
institution = {University of Namur},
}

@article{More_Sorensen_1983,
title = {Computing a trust region step},
author = {Mor{\'e}, J. J. and Sorensen, D.},
journal = sistc,
volume = {4},
pages = {553--572},
year = {1983},
}

@article{Byrd_Schnabel_Shultz_1988,
title = {Approximate solution of the trust region problem by minimization over two-dimensional subspaces},
author = {Byrd, R. H. and Schnabel, R. and Shultz, G. A.},
journal = mprog, 
volume = {40},
pages = {247--263},
year = {1988},
}

@incollection{Powell_1970a,
address = {London},
author = {Powell, M. J. D.},
booktitle = {Numerical Methods for Nonlinear Algebraic Equations},
editor = {Rabinowitz, P.},
pages = {87--114},
publisher = {Gordon \& Breach Science},
title = {A hybrid method for nonlinear equations},
year = {1970}
}

@incollection{Powell_1970b,
address = {London},
author = {Powell, M. J. D.},
booktitle = {Numerical Methods for Nonlinear Algebraic Equations},
editor = {Rabinowitz, P.},
pages = {115--161},
publisher = {Gordon \& Breach Science},
title = {A {Fortran} Subroutine for Solving Systems of Nonlinear
Algebraic Equations},
year = {1970}
}

@article{Dennis_Mei_1979,
title = {Two new unconstrained optimization algorithms which use function and gradient values},
author = {{Dennis, Jr.}, J. E. and Mei, H.},
journal = jota,
volume = {28},
pages = {453--482},
year = {1979},
publisher = {Springer}
}

@article{Steihaug_1983,
title = {The conjugate gradient method and trust regions in large scale optimization},
author = {Steihaug, T.},
journal = sinum,
volume = {20},
pages = {626--637},
year = {1983},
}

@article{Birgin_Gardenghi_Martinez_Toint_2017,
title = {Worst-case evaluation complexity for unconstrained
nonlinear optimization using high-order regularized models},
author = {Birgin, E. G. and Gardenghi, J. L. and Mart\'{i}nez, J. M. and
Santos, S. A.  and Toint, Ph. L.},
journal = mprog, 
year = {2017},
volume = {163}, 
pages = {359--368}
}

@phdthesis{Thomas_1975,
title = {Sequential Estimation Techniques for Quasi-{Newton} Algorithms},
author = {Thomas, S. W.},
year = {1975},
school = {Cornell University},
address = {New York}
}

@incollection{Yuan_1998,
title = {An example of non-convergence of trust region algorithms},
author = {Yuan, Y.},
editor = {Yuan, Y.},
booktitle = {Advances in Nonlinear Programming},
pages = {205--215},
year = {1998},
publisher = {Kluwer Academic Publishers},
address = {Dordrecht}
}

@techreport{Griewank_1981,
title = {The modification of {Newton}'s method for unconstrained
optimization by bounding cubic terms},
author = {Griewank, A.},
number = {Technical Report NA/12},
year = {1981},
institution = {DAMTP, University of Cambridge},
}

@article{Nesterov_Polyak_2006,
title = {Cubic regularization of {Newton} method and its global performance},
author = {Nesterov, Yu. and Polyak, B. T.},
journal = mprog,
volume = {108},
pages = {177--205},
year = {2006},
}

@article{Cartis_Gould_Toint_2011a,
title = {Adaptive cubic regularisation methods for unconstrained optimization. {Part I}: motivation, convergence and numerical
results},
author = {Cartis, C. and Gould, N. I. M. and Toint, Ph. L.},
journal = mprog,
volume = {127},
pages = {245--295},
year = {2011},
}

@article{Cartis_Gould_Toint_2011b,
title = {Adaptive cubic regularisation methods for unconstrained optimization. {Part II}: worst-case function-and derivative-evaluation complexity},
author = {Cartis, C. and Gould, N. I. M. and Toint, Ph. L.},
journal = mprog,
volume = {130},
pages = {295--319},
year = {2011},
}

@article{Heinkenschloss_Vicent_2002,
title = {Analysis of inexact trust-region {SQP} algorithms},
author = {Heinkenschloss, M. and Vicente, L. N.},
journal = siopt,
volume = {12},
pages = {283--302},
year = {2002},
publisher = {SIAM}
}

@article{Dennis_More_1977,
title = {{Quasi-Newton} methods, motivation and theory},
author = {Dennis, Jr., J. E. and Mor{\'e}, J. J.},
journal = sirev,
volume = {19},
pages = {46--89},
year = {1977},
}

@book{HighamNJ_2002,
title = {Accuracy and Stability of Numerical Algorithms},
author = {Higham, N. J.},
year = {2002},
edition = {Second},
publisher = {SIAM},
address = {Philadelphia}
}

@book{Rockafellar_1970,
title = {Convex Analysis},
author = {Rockafellar, R. T.},
year = {1970},
publisher = {Princeton University Press},
address = {New Jersey}
}

@book{Rockafellar_Wets_1998,
title = {Variational Analysis},
author = {Rockafellar, R. T. and Wets, R. J.-B.},
year = {1998},
publisher = {Springer},
address = {Berlin}
}

@TechReport{Leyffer_etal_2016,
author = {Leyffer, S. and Wild, S. M. and Fagan, M. and
Snir, M. and Palem, K. and Finkel, H. and Yoshii, K.},
title = {Doing {Moore} with Less -- Leapfrogging {Moore's} Law with Inexactness for Supercomputing},
institution = {Argonne National Laboratory MCS},
year = {2016},
number = {ANL/MCS-P6077-1016},
}

@article{Palem_2014,
title = {Inexactness and a future of computing},
author = {Palem, K. V.},
journal = {Phil. Trans. R. Soc. A},
volume = {372},
pages = {20130281},
year = {2014},
}

@article{BaboulinM_etal_2009,
title = {Accelerating scientific computations with mixed precision
algorithms},
author = {Baboulin, M. and Buttari, A. and Dongarra, J.
and Kurzak, J. and Langou, J. and Langou, J. and
Luszczek, P. and Tomov, S.},
journal = {Comput. Phys. Commun.},
volume = {180},
pages = {2526-2533},
year = {2009},
}

@article{LKugler_2015,
title = {Is ``good enough'' computing good enough?},
author = {Kugler, L.},
journal = cacm,
volume = {58},
pages = {12-14},
year = 2015,
}

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