Large-scale Nonlinear Constrained Optimization: a Current Survey

Much progress has been made in constrained nonlinear optimization in the past ten years, but most large-scale problems still represent a considerable obstacle.

[1]  M. Lescrenier.  Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold , 1991 .

[2]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[3]  P. Boggs,et al.  A strategy for global convergence in a sequential quadratic programming algorithm , 1989 .

[4]  T. Coleman,et al.  On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds , 1992 .

[5]  T. Coleman,et al.  A Global and Quadratic Affine Scaling Method for Linear $L_{1}$ Problems. , 1989 .

[6]  I. Duff.  Sparse Matrices and Their Uses. , 1983 .

[7]  Andrew R. Conn,et al.  Nonlinear programming via an exact penalty function: Global analysis , 1982, Math. Program..

[8]  Ronald D. Armstrong,et al.  Lagrangian approach for large-scale least absolute value estimation , 1993, Comput. Oper. Res..

[9]  W. Murray,et al.  Newton methods for large-scale linear equality-constrained minimization , 1993 .

[10]  T. Coleman,et al.  A global and quadratically convergent method for linear l ∞ problems , 1992 .

[11]  P. Toint,et al.  Partitioned variable metric updates for large structured optimization problems , 1982 .

[12]  Boris Polyak,et al.  Constrained minimization methods , 1966 .

[13]  Stephen G. Nash,et al.  A General-Purpose Parallel Algorithm for Unconstrained Optimization , 1991, SIAM J. Optim..

[14]  Stephen J. Wright,et al.  Optimization Software Guide , 1987 .

[15]  W. Hager.  Multiplier methods for nonlinear optimal control , 1990 .

[16]  Garth P. McCormick,et al.  Communications to the Editor--Exponential Forecasting: Some New Variations , 1969 .

[17]  D. A. Schrady,et al.  Models for multi‐item continuous review inventory policies subject to constraints , 1971 .

[18]  S. M. Robinson,et al.  A quadratically-convergent algorithm for general nonlinear programming problems , 1972, Math. Program..

[19]  Joaquim Júdice,et al.  A block principal pivoting algorithm for large-scale strictly monotone linear complementarity problems , 1994, Comput. Oper. Res..

[20]  Margaret H. Wright,et al.  Optimization and large-scale computation , 1991 .

[21]  Jorge J. Moré,et al.  Recent Developments in Algorithms and Software for Trust Region Methods , 1982, ISMP.

[22]  K. Tanabe,et al.  Mathematical Programming: Recent Developments and Applications. , 1990 .

[23]  S. Nash,et al.  A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization , 1994 .

[24]  Martin P. Bendsøe,et al.  A New Method for Optimal Truss Topology Design , 1993, SIAM J. Optim..

[25]  Philippe L. Toint,et al.  Towards an efficient sparsity exploiting newton method for minimization , 1981 .

[26]  L. C. W. Dixon,et al.  On Automatic Differentiation and Continuous Optimization , 1994 .

[27]  Daniel Tuyttens,et al.  LSNNO, a FORTRAN subroutine for solving large-scale nonlinear network optimization problems , 1992, TOMS.

[28]  P. Toint,et al.  Testing a class of methods for solving minimization problems with simple bounds on the variables , 1988 .

[29]  Thomas F. Coleman,et al.  Large-Scale Numerical Optimization , 1990 .

[30]  Mustafa Ç. Pinar,et al.  Parallel Block-Partitioning of Truncated Newton for Nonlinear Network Optimization , 1992, SIAM J. Sci. Comput..

[31]  Andreas Griewank,et al.  On the unconstrained optimization of partially separable functions , 1982 .

[32]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

[33]  Walter Murray,et al.  Line Search Procedures for the Logarithmic Barrier Function , 1994, SIAM J. Optim..

[34]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

[35]  John T. Betts,et al.  A performance comparison of nonlinear programming algorithms for large sparse problems , 1993 .

[36]  J. C. Dunn.  Second-Order Multiplier Update Calculations for Optimal Control Problems and Related Large Scale Nonlinear Programs , 1993, SIAM J. Optim..

[37]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[38]  J. Júdice.  Algorithms for Linear Complementarity Problems , 1994 .

[39]  Ron S. Dembo,et al.  The performance of NLPNET, a large-scale nonlinear network optimizer , 1986 .

[40]  Thomas F. Coleman,et al.  Parallel structural optimization applied to bone remodeling on distributed memory machines , 1995, Comput. Optim. Appl..

[41]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[42]  Linda Kaufman,et al.  Separable Nonlinear Least Squares with Multiple Right-Hand Sides , 1992, SIAM J. Matrix Anal. Appl..

[43]  Michael A. Saunders,et al.  Preconditioners for Indefinite Systems Arising in Optimization , 1992, SIAM J. Matrix Anal. Appl..

[44]  Robert J. Vanderbei,et al.  Symmetric indefinite systems for interior point methods , 1993, Math. Program..

[45]  Paul H. Calamai,et al.  A projection method forlp norm location-allocation problems , 1994, Math. Program..

[46]  P. Toint,et al.  A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization , 1994 .

[47]  J. P. Hennart,et al.  Advances in Numerical Partial Differential Equations and Optimization: Proceedings of the Fifth Mexico-United States Workshop , 1991 .

[48]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[49]  Guoliang Xue,et al.  The MINPACK-2 test problem collection , 1992 .

[50]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[51]  Nicholas I. M. Gould,et al.  Global Convergence of a Class of Trust Region Algorithms for Optimization Using Inexact Projections on Convex Constraints , 1993, SIAM J. Optim..

[52]  Jorge Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[53]  Robert M. Freund,et al.  Theoretical efficiency of a shifted-barrier-function algorithm for linear programming , 1991 .

[54]  Iain S. Duff,et al.  MA28 --- A set of Fortran subroutines for sparse unsymmetric linear equations , 1980 .

[55]  Yuying Li,et al.  A Globally Convergent Method for lp Problems , 1991, SIAM J. Optim..

[56]  Michael A. Saunders,et al.  Transformed Hessian methods for large-scale constrained optimization , 1994 .

[57]  Åke Björck,et al.  Generalized and Sparse Least Squares Problems , 1994 .

[58]  David F. Shanno,et al.  Remark on “Algorithm 500: Minimization of Unconstrained Multivariate Functions [E4]” , 1980, TOMS.

[59]  A. P. Jones.  THE CHEMICAL EQUILIBRIUM PROBLEM: AN APPLICATION OF SUMT , 1967 .

[60]  Griewank,et al.  On automatic differentiation , 1988 .

[61]  Kristján Jónasson,et al.  Corrected sequential linear programming for sparse minimax optimization , 1994 .

[62]  Thomas F. Coleman,et al.  Large-Scale Numerical Optimization: Introduction and Overview , 1991 .

[63]  A. Griewank,et al.  Automatic differentiation of algorithms : theory, implementation, and application , 1994 .

[64]  Jack Belzer,et al.  Encyclopedia of Computer Science and Technology , 2002 .

[65]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[66]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[67]  Nicholas I. M. Gould,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[68]  Gerardo Toraldo,et al.  On the Solution of Large Quadratic Programming Problems with Bound Constraints , 1991, SIAM J. Optim..

[69]  M. C. Bartholomew-Biggs,et al.  Algorithms for General Constrained Nonlinear Optimization , 1994 .

[70]  Nicholas I. M. Gould,et al.  Large-scale nonlinear constrained optimization , 1992 .

[71]  Thomas F. Coleman,et al.  A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables , 1992, SIAM J. Optim..

[72]  W. Murray,et al.  Efficient Linear Search Algorithms for the Logarithmic Barrier Function , 1976 .

[73]  Thomas F. Coleman,et al.  An efficient trust region method for unconstrained discrete-time optimal control problems , 1995, Comput. Optim. Appl..

[74]  W. Hager,et al.  Large Scale Optimization : State of the Art , 1993 .

[75]  R. Glowinski,et al.  Computing Methods in Applied Sciences and Engineering , 1974 .

[76]  Yuying Li.  Solving $L_{p}$-Norm Problems and Applications , 1993 .

[77]  L. Biegler.  Optimization Strategies for Complex Process Models , 1992 .

[78]  Garth P. McCormick,et al.  Optimization with unary functions , 1991, Math. Program..

[79]  J. J. Moré,et al.  Algorithms for bound constrained quadratic programming problems , 1989 .

[80]  Stavros A. Zenios,et al.  Parallel Numerical Optimization: Current Status and an Annotated Bibliography , 1989, INFORMS J. Comput..

[81]  Jorge Nocedal,et al.  A Reduced Hessian Method for Large-Scale Constrained Optimization , 1995, SIAM J. Optim..

[82]  G. McCormick,et al.  Computational Aspects of the International Coal Trade Model , 1985 .

[83]  M. J. D. Powell,et al.  Nonlinear optimization, 1981 , 1982 .

[84]  A. Sluis.  Condition numbers and equilibration of matrices , 1969 .

[85]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[86]  Roman A. Polyak,et al.  Modified barrier functions (theory and methods) , 1992, Math. Program..

[87]  R. Schnabel,et al.  Tensor Methods for Nonlinear Equations. , 1984 .

[88]  Michael R. Osborne,et al.  A modified barrier function method with improved rate of convergence for degenerate problems , 1980, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[89]  Philip E. Gill,et al.  Newton-type methods for unconstrained and linearly constrained optimization , 1974, Math. Program..

[90]  T. Chan,et al.  Computing a search direction for large scale linearly constrained nonlinear optimization calculations , 1993 .

[91]  M. Powell.  A New Algorithm for Unconstrained Optimization , 1970 .

[92]  Zhijun Wu,et al.  The Eeective Energy Transformation Scheme as a General Continuation Approach to Global Optimization with Application to Molecular Conformation , 2022 .

[93]  François-Xavier Le Dimet,et al.  Numerical Experience with Limited-Memory Quasi-Newton and Truncated Newton Methods , 1993, SIAM J. Optim..

[94]  Laurie A. Hulbert,et al.  A direct active set algorithm for large sparse quadratic programs with simple bounds , 1989, Math. Program..

[95]  Leon S. Lasdon,et al.  Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming , 1978, TOMS.

[96]  Thomas F. Coleman,et al.  Isotropic effective energy simulated annealing searches for low energy molecular cluster states , 1993, Comput. Optim. Appl..

[97]  Laurie A. Hulbert,et al.  A Globally and Superlinearly Convergent Algorithm for Convex Quadratic Programs with Simple Bbounds , 1993, SIAM J. Optim..

[98]  R. Dembo.  A primal truncated newton algorithm with application to large-scale nonlinear network optimization , 1987 .

[99]  John M. Mulvey,et al.  Nonlinear Network Programming on Vector Supercomputers: A Study on the CRAY X-MP , 1986, Oper. Res..

[100]  Karl Kunisch,et al.  Reduced SQP methods for parameter identification problems , 1992 .

[101]  M. D. Hebden,et al.  An algorithm for minimization using exact second derivatives , 1973 .

[102]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[103]  J. Betts,et al.  A sparse nonlinear optimization algorithm , 1994 .

[104]  T. Coleman,et al.  On the Local Convergence of a Quasi-Newton Method for the Nonlinear Programming Problem , 1984 .

[105]  R. Daniel.  Parallel Nonlinear Optimization , 1990, Proceedings of the Fifth Distributed Memory Computing Conference, 1990..

[106]  M. Powell.  CONVERGENCE PROPERTIES OF A CLASS OF MINIMIZATION ALGORITHMS , 1975 .

[107]  P. Toint,et al.  Performance of a multifrontal scheme for partially separable optimization , 1994 .

[108]  Nicholas I. M. Gould,et al.  A note on exploiting structure when using slack variables , 1994, Math. Program..

[109]  M. J. D. Powell,et al.  Some Convergence Properties of the Modified Log Barrier Method for Linear Programming , 1995, SIAM J. Optim..

[110]  John M. Mulvey,et al.  Nonlinear programming on generalized networks , 1987, TOMS.

[111]  P. Toint,et al.  Local convergence analysis for partitioned quasi-Newton updates , 1982 .

[112]  Nicholas I. M. Gould,et al.  Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints , 1996, SIAM J. Optim..

[113]  Paul H. Calamai,et al.  A projected newton method forlp norm location problems , 1987, Math. Program..

[114]  John M. Mulvey,et al.  Vectorization and multitasking of nonlinear network programming algorithms , 1988, Math. Program..

[115]  J. L’Excellent,et al.  On the use of element-by-element preconditioners to solve large scale partially separable optimization problems , 1995 .

[116]  B. M. Averick,et al.  The MINPACK-2 test problem collection (preliminary version) , 1991 .

[117]  Daniel Tuyttens,et al.  On large scale nonlinear Network optimization , 1990, Math. Program..

[118]  Andreas Griewank,et al.  Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++ , 1996, TOMS.

[119]  Panos M. Pardalos,et al.  Large Scale Optimization , 1994 .

[120]  Stephen G. Nash,et al.  A Barrier Method for Large-Scale Constrained Optimization , 1993, INFORMS J. Comput..

[121]  Trond Steihaug.  Local and superlinear convergence for truncated iterated projections methods , 1983, Math. Program..

[122]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[123]  Elizabeth Eskow,et al.  A New Modified Cholesky Factorization , 1990, SIAM J. Sci. Comput..

[124]  P. Toint,et al.  Local Convergence Properties of two Augmented Lagrangian Algorithms for Optimization with a Combinat , 1993 .

[125]  P. Toint,et al.  On Large Scale Nonlinear Least Squares Calculations , 1987 .

[126]  M. J. D. Powell,et al.  Nonlinear Programming—Sequential Unconstrained Minimization Techniques , 1969 .

[127]  Richard H. Byrd,et al.  Analysis of a Symmetric Rank-One Trust Region Method , 1996, SIAM J. Optim..

[128]  D. Bertsekas.  Projected Newton methods for optimization problems with simple constraints , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[129]  John K. Reid,et al.  The Multifrontal Solution of Indefinite Sparse Symmetric Linear , 1983, TOMS.

[130]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[131]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[132]  Jill P. Mesirov.  Very large scale computation in the 21st century , 1992 .

[133]  David F. Shanno,et al.  Preliminary Computational Experience with Modified Log-Barrier Functions for Large-Scale Nonlinear Programming , 1994 .

[134]  P. Toint,et al.  Improving the Decomposition of Partially Separable Functions in the Context of Large-Scale Optimization: a First Approach· , 1993 .

[135]  Gene H. Golub,et al.  Linear algebra for large scale and real-time applications , 1993 .

[136]  David L. Jensen,et al.  The convergence of a modified barrier method for convex programming , 1994, IBM J. Res. Dev..

[137]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[138]  Martin P. Bendsøe,et al.  Equivalent displacement based formulations for maximum strength truss topology design , 1992, IMPACT Comput. Sci. Eng..

[139]  Peter Nash.  Systems modelling and optimization , 1981 .

[140]  Paul E. Plassmann,et al.  A Parallel Nonlinear Least-Squares Solver: Theoretical Analysis and Numerical Results , 1992, SIAM J. Sci. Comput..

[141]  Ph. L. Toint,et al.  A sparse quasi-Newton update derived variationally with a nondiagonally weighted Frobenius norm , 1981 .

[142]  Thomas F. Coleman,et al.  A globally and quadratically convergent affine scaling method for linearℓ1 problems , 1992, Math. Program..

[143]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

[144]  G. Golub,et al.  A comparison between some direct and iterative methods for certian large scale godetic least squares problems , 1986 .

[145]  Nicholas I. M. Gould,et al.  Numerical experiments with the LANCELOT package (release A) for large-scale nonlinear optimization , 1996, Math. Program..

[146]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[147]  T. Steihaug.  The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[148]  P. Gill,et al.  Large-scale SQP methods and their application in trajectory optimization , 1994 .

[149]  CarleAlan,et al.  ADIFOR-Generating Derivative Codes from Fortran Programs , 1992 .

[150]  S. K. Eldersveld.  Large-scale sequential quadratic programming algorithms , 1992 .

[151]  Nicholas I. M. Gould,et al.  On Iterated-Subspace Minimization Methods for Nonlinear Optimization , 1996 .

[152]  Bobby Schnabel,et al.  A modular system of algorithms for unconstrained minimization , 1985, TOMS.

[153]  D. Sorensen.  An example concerning quasi-Newton estimation of a sparse hessian , 1981, SGNM.

[154]  Nicholas I. M. Gould,et al.  Convergence Properties of Minimization Algorithms for Convex Constraints Using a Structured Trust Region , 1996, SIAM J. Optim..

[155]  Ali Bouaricha.  Tensor-Krylov methods for large nonlinear equations , 1996, Comput. Optim. Appl..

[156]  P. J. Werbos,et al.  Backpropagation: past and future , 1988, IEEE 1988 International Conference on Neural Networks.

[157]  Andreas Griewank,et al.  ADIFOR: A Fortran system for portable automatic differentiation , 1992 .

[158]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[159]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[160]  E. Omojokun.  Trust region algorithms for optimization with nonlinear equality and inequality constraints , 1990 .

[161]  Iain S. Duff,et al.  MA27 -- A set of Fortran subroutines for solving sparse symmetric sets of linear equations , 1982 .

[162]  Bobby Schnabel,et al.  Tensor Methods for Unconstrained Optimization Using Second Derivatives , 1991, SIAM J. Optim..

[163]  P. Toint,et al.  A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds , 1991 .

[164]  E. Spedicato.  Algorithms for continuous optimization : the state of the art , 1994 .

[165]  Tamar Schlick,et al.  Modified Cholesky Factorizations for Sparse Preconditioners , 1993, SIAM J. Sci. Comput..

[166]  M. C. Bartholomew-Biggs,et al.  Modifications to the subroutine OPALQP for dealing with large problems , 1994 .

[167]  Jorge Nocedal,et al.  Representations of quasi-Newton matrices and their use in limited memory methods , 1994, Math. Program..

[168]  Stuart Smith,et al.  Solving Large Sparse Nonlinear Programs Using GRG , 1992, INFORMS J. Comput..

[169]  Paul E. Plassmann,et al.  Solution of Nonlinear Least Squares Problems on a Multiprocessor , 1988, Shell Conference.

[170]  Annick Sartenaer,et al.  A Class of Trust Region Methods for Nonlinear Network Optimization Problems , 1995, SIAM J. Optim..

[171]  Achiya Dax.  A row relaxation method for large minimax problems , 1993 .

[172]  P. Toint,et al.  Global convergence of a class of trust region algorithms for optimization with simple bounds , 1988 .

[173]  N. Gould.  An Algorithm for Large-Scale Quadratic Programming , 1991 .

[174]  John D. Ramsdell,et al.  Estimation of Sparse Jacobian Matrices , 1983 .

[175]  Robert B. Schnabel,et al.  TENSOLVE: A Software Package for Solving Systems at Nonlinear Equations and Nonlinear Least Squares Problems Using Tensor Methods ; CU-CS-735-94 , 1994 .

[176]  J. Davenport.  Editor , 1960 .