The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Computing Optimal Locally Constrained Steps
Abstract
In seeking to solve an unconstrained minimization problem, one often computes steps based on a quadratic approximation q to the objective function. A reasonable way to choose such steps is by minimizing q constrained to a neighborhood of the current iterate. This paper considers ellipsoidal neighborhoods and presents a new way to handle certain computational details when the Hessian of q is indefinite, paying particular attention to a special case which may then arise. The proposed step computing algorithm provides an attractive way to deal with negative curvature. Implementations of this algorithm have proved very satisfactory in the nonlinear least-squares solves NL2SOL.
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Citations
Cites
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
A method for the solution of certain non-linear problems in least squares
Levenberg, K. (1944) · Quarterly of Applied Mathematics · doi:10.1090/qam/10666 · Cited by 12,359
Introduction to matrix computations
Stewart, G. W. (1973) · International Linear Collider · Cited by 2,381
Reinsch, C. H. (1967) · Numerische Mathematik · doi:10.1007/bf02162161 · Cited by 2,236
Testing Unconstrained Optimization Software
Morè, J. J., Garbow, B. S., & Hillstrom, K. E. (1981) · ACM Transactions on Mathematical Software · doi:10.1145/355934.355936 · Cited by 1,527
An Adaptive Nonlinear Least-Squares Algorithm
Dennis, J. E., Gay, D. M., & Walsh, R. E. (1981) · ACM Transactions on Mathematical Software · doi:10.1145/355958.355965 · Cited by 930
Self-citationMaximization by Quadratic Hill-Climbing
Goldfeld, S. M., Quandt, R. E., & Trotter, H. F. (1966) · Econometrica · doi:10.2307/1909768 · Cited by 364
Smoothing by spline functions. II
Reinsch, C. H. (1971) · Numerische Mathematik · doi:10.1007/bf02169154 · Cited by 333
Cited by
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Coleman, T. F., & Li, Y. (1996) · SIAM Journal on Optimization · doi:10.1137/0806023 · Cited by 3,320
Iterative Methods for Optimization
Kelley, C. T. (1999) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970920 · Cited by 2,052
Sequential quadratic programming
Boggs, P. T., & Tolle, J. W. (1995) · Acta Numerica · doi:10.1017/s0962492900002518 · Cited by 1,858
Approximate solution of the trust region problem by minimization over two-dimensional subspaces
Byrd, R. H., Schnabel, R. B., & Shultz, G. A. (1988) · Mathematical Programming · doi:10.1007/bf01580735 · Cited by 411
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
Dennis, J. E., Gay, D. M., & Welsch, R. E. (1981) · ACM Transactions on Mathematical Software · doi:10.1145/355958.355966 · Cited by 405
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Metadata
- Authors
- Gay, D. M.
- Venue
- SIAM Journal on Scientific and Statistical Computing
- Published
- 1981-06
- Volume
- 2
- Issue
- 2
- Pages
- 186-197
- ISSN
- 0196-5204 (ISSN-L)
- 2168-3417
- OpenAlex
- W3003775594
- Cited by
- 293
- References
- 8
- FWCI
- 6.40
- Type
- journal article
- Language
- en
- Open access
- closed
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