An iterative working-set method for large-scale nonconvex quadratic programming

[1]  A. Forsgren Inertia-controlling factorizations for optimization algorithms , 2002 .

[2]  P. Toint,et al.  Numerical Methods for Large-Scale Non-Convex Quadratic Programming , 2002 .

[3]  Nicholas I. M. Gould,et al.  On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization , 2001, SIAM J. Sci. Comput..

[4]  Nicholas I. M. Gould,et al.  A primal-dual trust-region algorithm for non-convex nonlinear programming , 2000, Math. Program..

[5]  Nicholas I. M. Gould,et al.  On Modified Factorizations for Large-Scale Linearly Constrained Optimization , 1999, SIAM J. Optim..

[6]  Nicholas I. M. Gould,et al.  Solving the Trust-Region Subproblem using the Lanczos Method , 1999, SIAM J. Optim..

[7]  John G. Lewis,et al.  Accurate Symmetric Indefinite Linear Equation Solvers , 1999, SIAM J. Matrix Anal. Appl..

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

[9]  John G. Lewis,et al.  Proceedings of the Fifth SIAM Conference on Applied Linear Algebra , 1994 .

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

[11]  Michael A. Saunders,et al.  Inertia-Controlling Methods for General Quadratic Programming , 1991, SIAM Rev..

[12]  P. Toint Global Convergence of a a of Trust-Region Methods for Nonconvex Minimization in Hilbert Space , 1988 .

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

[14]  P. Gill,et al.  A Schur-complement method for sparse quadratic programming , 1987 .

[15]  Paul H. Calamai,et al.  Projected gradient methods for linearly constrained problems , 1987, Math. Program..

[16]  Nicholas I. M. Gould,et al.  On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem , 1985, Math. Program..

[17]  J. Crouzeix,et al.  Definiteness and semidefiniteness of quadratic forms revisited , 1984 .

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

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

[20]  R. Fletcher A model algorithm for composite nondifferentiable optimization problems , 1982 .

[21]  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.

[22]  Philip E. Gill,et al.  Practical optimization , 1981 .

[23]  Shih-Ping Han SOLVING QUADRATIC PROGRAMS BY AN EXACT PENALTY FUNCTION , 1981 .

[24]  Magnus R. Hestenes,et al.  Conjugate Direction Methods in Optimization , 1980 .

[25]  Regina Benveniste A quadratic programming algorithm using conjugate search directions , 1979, Math. Program..

[26]  I. Duff,et al.  Direct Solution of Sets of Linear Equations whose Matrix is Sparse, Symmetric and Indefinite , 1979 .

[27]  Alexander Meeraus,et al.  Matrix augmentation and partitioning in the updating of the basis inverse , 1977, Math. Program..

[28]  D. Sorensen Updating the Symmetric Indefinite Factorization with Applications in a Modified Newton's Method , 1977 .

[29]  Klaus Ritter,et al.  An effective algorithm for quadratic minimization problems , 1976 .

[30]  R. Fletcher Factorizing symmetric indefinite matrices , 1976 .

[31]  J. Bunch,et al.  Some stable methods for calculating inertia and solving symmetric linear systems , 1977 .

[32]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

[33]  J. Bunch,et al.  Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations , 1971 .

[34]  Boris Polyak The conjugate gradient method in extremal problems , 1969 .

[35]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .