Bertsekas, D. P. (1980), ‘Variable metric methods for constrained optimization based on differentiable exact penalty functions’, in Proceedings of the Eighteenth Allerton Conference on Communications, Control and Computing, Allerton Park, Illinois, pp. 584–593.
Bertsekas, D. P. (1982), Constrained Optimization and Lagrange Multipliers Methods, Academic Press, London.
Boggs, P. T., Domich, P. D., Rogers, J. E. and Witzgall, C. (1991), ‘An interior point method for linear and quadratic programming problems’, Mathematical Programming Society Committee on Algorithms Newsletter 19, 32–40.
Boggs, P. T., Domich, P. D., Rogers, J. E. and Witzgall, C. (1994), ‘An interior-point method for general large scale quadratic programming problems’, Internal report (in progress), National Institute of Standards and Technology.
Boggs, P. T. and Tolle, J. W. (1980), ‘Augmented Lagrangians which are quadratic in the multiplier’, Journal of Optimization Theory and Applications 31, 17–26.
Boggs, P. T. and Tolle, J. W. (1984), ‘A family of descent functions for constrained optimization’, SIAM Journal on Numerical Analysis 21, 1146–1161.
Boggs, P. T. and Tolle, J. W. (1989), ‘A strategy for global convergence in a sequential quadratic programming algorithm’, SIAM Journal on Numerical Analysis 21, 600–623.
Boggs, P. T. and Tolle, J. W. (1994), ‘Convergence properties of a class of rank-two updates’, SIAM Journal on Optimization 4, 262–287.
Boggs, P. T., Tolle, J. W. and Kearsley, A. J. (1991), ‘A merit function for inequality constrained nonlinear programming problems’, Internal Report 4702, National Institute of Standards and Technology.
Boggs, P. T., Tolle, J. W. and Kearsley, A. J. (1994), ‘A practical algorithm for general large scale nonlinear optimization problems’, Internal report, National Institute of Standards and Technology.
Boggs, P. T., Tolle, J. W. and Wang, P. (1982), ‘On the local convergence of quasi-Newton methods for constrained optimization’, SIAM Journal on Control and Optimization 20, 161–171.
Bonnans, J. F., Panier, E. R., Tits, A. L. and Zhou, J. L. (1992), ‘Avoiding the Maratos effect by means of a nonmonotone line search II. Inequality constrained problems—feasible iterates’, SIAM Journal on Numerical Analysis 29, 1187–1202.
Broyden, C. G., Dennis, J. E. Jr and Moré, J. J. (1973), ‘On the local and superlinear convergence of quasi-Newton methods’, Journal of the Institute of Mathematical Applications 12, 223–246.
Byrd, R. H. and Nocedal, J. (1991), ‘An analysis of reduced Hessian methods for constrained optimization’, Mathematical Programming 49, 285–323.
Byrd, R. H. and Schnabel, R. B. (1986), ‘Continuity of the null space basis and constrained optimization’, Mathematical Programming 35, 32–41.
Byrd, R. H., Schnabel, R. B. and Schultz, G. A. (1985), ‘A trust-region strategy for nonlinearly constrained optimization’, SIAM Journal on Numerical Analysis 24, 1152–1170.
Byrd, R. H., Tapia, R. A. and Zhang, Y. (1992), ‘An SQP augmented Lagrangian BFGS algorithm for constrained optimization’, SIAM Journal on Optimization 2, 210–241.
Celis, M. R., Dennis, J. E. Jr and Tapia, R. A. (1985), ‘A trust-region strategy for nonlinear equality constrained optimization’, in Numerical Optimization 1984 (Boggs, P., Byrd, R. and Schnabel, R., eds.), SIAM, Philadelphia, pp. 71–82.
Chamberlain, R., Lemarechal, C., Pedersen, H. C. and Powell, M. J. D. (1982), ‘The watchdog technique for forcing convergence in algorithms for constrained optimization’, Mathematical Programming Study 16, 1–17.
Coleman, T. F. (1990), ‘On characterizations of superlinear convergence for constrained optimization’, in Lectures in Applied Mathematics, American Mathematical Society, Providence, Rhode Island, pp. 113–133.
Coleman, T. F. and Conn, A. R. (1984), ‘On the local convergence of a quasi-Newton method for the nonlinear programming problem’, SIAM Journal on Numerical Analysis 21, 755–769.
Coleman, T. F. and Feynes, P. A. (1992), ‘Partitioned quasi-Newton methods for nonlinear equality constrained optimization’, Mathematical Programming 53, 17–44.
Coleman, T. F. and Sorensen, D. C. (1984), ‘A note on the computation of an orthonormal basis for the null space of a matrix’, Mathematical Programming 29, 234–242.
Dennis, J. E. Jr and Moré, J. J. (1977), ‘Quasi-Newton methods, motivation and theory’, SIAM Review 19, 46–89.
Dennis, J. E. Jr and Schnabel, R. B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey.
El-Alem, M. M. (1991), ‘A global convergence theory for the Celis-Dennis-Tapia trust region algorithm for constrained optimization’, SIAM Journal on Numerical Analysis 28, 266–290.
El-Alem, M. M. (1992), ‘A robust trust region algorithm with nonmonotonic penalty parameter scheme for constrained optimization’, Department of Mathematical Sciences 92–30, Rice University.
Fletcher, R. (1972), ‘A class of methods for nonlinear programming, iii: Rates of convergence’, in Numerical Methods for Nonlinear Optimization (Lootsma, F. A., ed.), Academic Press, New York, pp. 371–382.
Fletcher, R. (1981), Practical Methods of Optimization, volume 2, Wiley, New York.
Fontecilla, R. (1988), ‘Local convergence of secant methods for nonlinear constrained optimization’, SIAM Journal on Numerical Analysis 25, 692–712.
Fontecilla, R., Steihaug, T. and Tapia, R. A. (1987), ‘A convergence theory for a class of quasi-Newton methods for constrained optimization’, SIAM Journal on Numerical Analysis 24, 1133–1151.
Fukushima, M. (1986), ‘A successive quadratic programming algorithm with global and superlinear convergence properties’, Mathematical Programming 35, 253–264.
Gabay, D. (1982), ‘Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization’, Mathematical Programming Study 16, 18–44.
Garcia-Palomares, U. M. and Mangasarian, O. L. (1976), ‘Superlinearly convergent quasi-Newton methods for nonlinearly constrained optimization problems’, Mathematical Programming 11, 1–13.
Gay, D. M. (1981), ‘Computing optimal locally constrained steps’, SIAM Journal on Scientific and Statistical Computing 2, 186–197.
Ge, R. and Powell, M. J. D. (1983), ‘The convergence of variable metric matrices in unconstrained optimization’, Mathematical Programming 27, 123–143.
Gilbert, J. C. (1993), ‘Superlinear convergence of a reduced BFGS method with piecewise line-search and update criterion’, Rapport de Recherche 2140, Institut National de Recherche en Informatique et en Automatique.
Gill, P. E., Murray, W., Saunders, M. A., Stewart, G. W. and Wright, M. H. (1985), ‘Properties of a representation of a basis for the null space’, Mathematical Programming 33, 172–186.
Gill, P. E., Murray, W., Saunders, M. A. and Wright, M. H. (1986), ‘User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming’, Technical Report SOL 2, Department of Operations Research, Stanford University.
Gill, P. E., Murray, W. and Wright, M. H. (1981), Practical Optimization, Academic Press, New York.
Glad, S. T. (1979), ‘Properties of updating methods for the multipliers in augmented Lagrangians’, Journal of Optimization Theory and Applications 28, 135–156.
Goodman, J. (1985), ‘Newton's method for constrained optimization’, Mathematical Programming 33, 162–171.
Grippo, L., Lampariello, F. and Lucidi, S. (1986), ‘A nonmonotone line search technique for Newton's method’, SIAM Journal on Numerical Analysis 23, 707–716.
Han, S.-P. (1976), ‘Superlinearly convergent variable metric algorithms for general nonlinear programming problems’, Mathematical Programming 11, 263–282.
Han, S.-P. (1977), ‘A globally convergent method for nonlinear programming’, Journal of Optimization Theory and Applications 22, 297–309.
Lalee, M., Nocedal, J. and Plantega, T. (1993), On the implementation of an algorithm for large-scale equality optimization, Department of Electrical Engineering and Computer Science NAM 09–93, Northwestern University.
Luenberger, D. G. (1984), Linear and Nonlinear Programming, 2d edition, Addison-Wesley, Reading, Massachusetts.
Moré, J. and Sorensen, D. C. (1983), ‘Computing a trust region step’, SIAM Journal of Scientific and Statistical Computing 4, 553–572.
Murray, W. (1994), ‘Algorithms for large nonlinear problems’, in Mathematical Programming: State of the Art 1994 (Birge, J. R. and Murty, K. G., eds.), University of Michigan, Ann Arbor, MI, pp. 172–185.
Murray, W. and Prieto, F. J. (1995), ‘A sequential quadratic programming algorithm using an incomplete solution of the subproblem’, SIAM Journal on Optimization, to appear.
Nash, S. G. and Sofer, A. (1995), Linear and Nonlinear Programming, McGraw-Hill, New York.
Nocedal, J. (1992), ‘Theory of algorithms for unconstrained optimization’, Acta Numerica 1991, 199–242.
Nocedal, J. and Overton, M. L. (1985), ‘Projected Hessian updating algorithms for nonlinearly constrained optimization problems’, SIAM Journal on Numerical Analysis 22, 821–850.
Omojokun, E. M. (1989), ‘Trust region algorithms for optimization with nonlinear equality and inequality constraints’, PhD thesis, University of Colorado.
Ortega, J. M. and Rheinboldt, W. C. (1970), Iterative Solution of Nonlinear Equations In Several Variables, Academic Press, New York.
Panier, E. R. and Tits, A. L. (1993), ‘On combining feasibility, descent and superlinear convergence in inequality constrained optimization’, Mathematical Programming 59, 261–276.
Polak, E. (1989), ‘Basics of minimax algorithms’, in Nonsmooth Optimization and Related Topics (Clark, F. H., Dem'yanov, V. F. and Giannessi, F., eds.), Plenum, New York, pp. 343–369.
Powell, M. J. D. (1977), ‘A fast algorithm for nonlinearly constrained optimization calculations’, in Numerical Analysis Dundee, 1977 (Watson, G. A., ed.), Springer-Verlag, Berlin, pp. 144–157.
Powell, M. J. D. (1978a), ‘Algorithms for nonlinear constraints that use Lagrangian functions’, Mathematical Programming 14, 224–248.
Powell, M. J. D. (1978b), ‘The convergence of variable metric methods for nonlinearly constrained optimization calculations’, in Nonlinear Programming 3 (Mangasarian, O., Meyer, R. and Robinson, S., eds.), Academic Press, New York, pp. 27–64.
Powell, M. J. D. and Yuan, Y. (1986), ‘A recursive quadratic programming algorithm that uses differentiable exact penalty functions’, Mathematical Programming 35, 265–278.
Robinson, S. M. (1974), ‘Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms’, Mathematical Programming 7, 1–16.
Schittkowski, K. (1981), ‘The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function, part 1: Convergence analysis’, Numerische Mathematik 38, 83–114.
Schittkowski, K. (1983), ‘On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function’, Math. Operationsforsch. U. Statist., Ser. Optimization 14, 197–216.
Stoer, J. (1984), ‘The convergence of matrices generated by rank-2 methods from the restricted β-class of Broyden’, Numerische Mathematik 44, 37–52.
Tapia, R. A. (1974), ‘A stable approach to Newton's method for optimization problems with equality constraints’, Journal of Optimization Theory and Applications 14, 453–476.
Tapia, R. A. (1977), ‘Diagonalized multiplier methods and quasi-Newton methods for constrained optimization’, Journal of Optimization Theory and Applications 22, 135–194.
Tapia, R. A. (1978), ‘Quasi-Newton methods for equality constrained optimization: Equivalence of existing methods and a new implementation’, in Nonlinear Programming 3 (Mangasarian, O., Meyer, R. and Robinson, S., eds.), Academic Press, New York, pp. 125–164.
Tapia, R. A. (1988), ‘On secant updates for use in general constrained optimization’, Mathematics of Computation 51, 181–202.
Vanderbei, R. J. and Carpenter, T. J. (1993), ‘Symmetric indefinite systems for interior point methods’, Mathematical Programming 58, 1–32.
Vardi, A. (1985), ‘A trust-region algorithm for equality constrained minimization and implementation’, SIAM Journal on Numerical Analysis 22, 575–591.
Wilson, R. B. (1963), A simplicial algorithm for concave programming, PhD thesis, Harvard University.
Wolfe, P. (1975), ‘A method of conjugate subgradients for minimizing nondifferentiable functions’, in Mathematical Programming Study 3 (Balinski, M. and Wolfe, P., eds.), North-Holland, Amsterdam, pp. 145–173.
Yuan, Y. (1985), ‘An only 2-step q-superlinear convergence example for some algorithms that use reduced Hessian approximations’, Mathematical Programming 32, 224–231.
Yuan, Y. (1990), ‘On a subproblem of trust region algorithms for constrained optimization’, Mathematical Programming 47, 53–63.