## Documentation Center |

[1] Biggs, M.C., "Constrained Minimization
Using Recursive Quadratic Programming," *Towards
Global Optimization* (L.C.W. Dixon and G.P. Szergo, eds.),
North-Holland, pp 341–349, 1975.

[2] Brayton, R.K., S.W. Director, G.D. Hachtel,
and L. Vidigal, "A New Algorithm for Statistical Circuit Design
Based on Quasi-Newton Methods and Function Splitting," *IEEE
Transactions on Circuits and Systems*, Vol. CAS-26, pp
784–794, Sept. 1979.

[3] Broyden, C.G., "The Convergence of
a Class of Double-rank Minimization Algorithms,"; *J.
Inst. Maths. Applics*., Vol. 6, pp 76–90, 1970.

[4] Conn, N.R., N.I.M. Gould, and Ph.L. Toint, *Trust-Region
Methods*, MPS/SIAM Series on Optimization, SIAM and MPS,
2000.

[5] Dantzig, G., *Linear Programming
and Extensions*, Princeton University Press, Princeton,
1963.

[6] Dantzig, G.B., A. Orden, and P. Wolfe, "Generalized
Simplex Method for Minimizing a Linear Form Under Linear Inequality
Restraints," *Pacific Journal Math.,* Vol.
5, pp. 183–195, 1955.

[7] Davidon, W.C., "Variable Metric Method
for Minimization," *A.E.C. Research and Development
Report*, ANL-5990, 1959.

[8] Dennis, J.E., Jr., "Nonlinear least-squares," *State
of the Art in Numerical Analysis* ed. D. Jacobs, Academic
Press, pp 269–312, 1977.

[9] Dennis, J.E., Jr. and R.B. Schnabel, *Numerical
Methods for Unconstrained Optimization and Nonlinear Equations*,
Prentice-Hall Series in Computational Mathematics, Prentice-Hall,
1983.

[10] Fleming, P.J., "Application of Multiobjective
Optimization to Compensator Design for SISO Control Systems," *Electronics
Letters*, Vol. 22, No. 5, pp 258–259, 1986.

[11] Fleming, P.J., "Computer-Aided Control
System Design of Regulators using a Multiobjective Optimization Approach," *Proc.
IFAC Control Applications of Nonlinear Prog. and Optim*.,
Capri, Italy, pp 47–52, 1985.

[12] Fletcher, R., "A New Approach to Variable
Metric Algorithms," *Computer Journal*,
Vol. 13, pp 317–322, 1970.

[13] Fletcher, R., "Practical Methods of Optimization," John Wiley and Sons, 1987.

[14] Fletcher, R. and M.J.D. Powell, "A
Rapidly Convergent Descent Method for Minimization," *Computer
Journal*, Vol. 6, pp 163–168, 1963.

[15] Forsythe, G.F., M.A. Malcolm, and C.B. Moler, *Computer
Methods for Mathematical Computations*, Prentice Hall,
1976.

[16] Gembicki, F.W., "Vector Optimization for Control with Performance and Parameter Sensitivity Indices," Ph.D. Thesis, Case Western Reserve Univ., Cleveland, Ohio, 1974.

[17] Gill, P.E., W. Murray, M.A. Saunders, and
M.H. Wright, "Procedures for Optimization Problems with a
Mixture of Bounds and General Linear Constraints," *ACM
Trans. Math. Software*, Vol. 10, pp 282–298, 1984.

[18] Gill, P.E., W. Murray, and M.H. Wright,* Numerical
Linear Algebra and Optimization*, Vol. 1, Addison Wesley,
1991.

[19] Gill, P.E., W. Murray, and M.H.Wright, *Practical
Optimization*, London, Academic Press, 1981.

[20] Goldfarb, D., "A Family of Variable
Metric Updates Derived by Variational Means," *Mathematics
of Computing*, Vol. 24, pp 23–26, 1970.

[21] Grace, A.C.W., "Computer-Aided Control System Design Using Optimization Techniques," Ph.D. Thesis, University of Wales, Bangor, Gwynedd, UK, 1989.

[22] Han, S.P., "A Globally Convergent
Method for Nonlinear Programming," *J. Optimization
Theory and Applications*, Vol. 22, p. 297, 1977.

[23] Hock, W. and K. Schittkowski, "A Comparative
Performance Evaluation of 27 Nonlinear Programming Codes," *Computing*,
Vol. 30, p. 335, 1983.

[24] Hollingdale, S.H., *Methods of
Operational Analysis in Newer Uses of Mathematics* (James
Lighthill, ed.), Penguin Books, 1978.

[25] Levenberg, K., "A Method for the Solution
of Certain Problems in Least Squares," *Quart. Appl.
Math*. Vol. 2, pp 164–168, 1944.

[26] Madsen, K. and H. Schjaer-Jacobsen, "Algorithms
for Worst Case Tolerance Optimization," *IEEE Transactions
of Circuits and Systems*, Vol. CAS-26, Sept. 1979.

[27] Marquardt, D., "An Algorithm for Least-Squares
Estimation of Nonlinear Parameters," *SIAM J. Appl.
Math*. Vol. 11, pp 431–441, 1963.

[28] Moré, J.J., "The Levenberg-Marquardt
Algorithm: Implementation and Theory," *Numerical
Analysis*, ed. G. A. Watson, Lecture Notes in Mathematics
630, Springer Verlag, pp 105–116, 1977.

[29] *NAG Fortran Library Manual,* Mark
12, Vol. 4, E04UAF, p. 16.

[30] Nelder, J.A. and R. Mead, "A Simplex
Method for Function Minimization,"* Computer J.,* Vol.7,
pp 308–313, 1965.

[31] Nocedal, J. and S. J. Wright. *Numerical
Optimization*, Second Edition. Springer Series in Operations
Research, Springer Verlag, 2006.

[32] Powell, M.J.D., "The Convergence of
Variable Metric Methods for Nonlinearly Constrained Optimization
Calculations," *Nonlinear Programming 3*,
(O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds.), Academic Press,
1978.

[33] Powell, M.J.D., "A Fast Algorithm
for Nonlinearly Constrained Optimization Calculations," *Numerical
Analysis*, G.A.Watson ed., Lecture Notes in Mathematics,
Springer Verlag, Vol. 630, 1978.

[34] Powell, M.J.D., "A Fortran Subroutine
for Solving Systems of Nonlinear Algebraic Equations," *Numerical
Methods for Nonlinear Algebraic Equations*, (P. Rabinowitz,
ed.), Ch.7, 1970.

[35] Powell, M.J.D., "Variable Metric Methods
for Constrained Optimization," *Mathematical Programming:
The State of the Art*, (A. Bachem, M. Grotschel and B.
Korte, eds.) Springer Verlag, pp 288–311, 1983.

[36] Schittkowski, K., "NLQPL: A FORTRAN-Subroutine
Solving Constrained Nonlinear Programming Problems," *Annals
of Operations Research*, Vol. 5, pp 485-500, 1985.

[37] Shanno, D.F., "Conditioning of Quasi-Newton
Methods for Function Minimization," *Mathematics
of Computing*, Vol. 24, pp 647–656, 1970.

[38] Waltz, F.M., "An Engineering Approach:
Hierarchical Optimization Criteria," *IEEE Trans*.,
Vol. AC-12, pp 179–180, April, 1967.

[39] Branch, M.A., T.F. Coleman, and Y. Li, "A
Subspace, Interior, and Conjugate Gradient Method for Large-Scale
Bound-Constrained Minimization Problems," *SIAM
Journal on Scientific Computing*, Vol. 21, Number 1, pp
1–23, 1999.

[40] Byrd, R.H., J. C. Gilbert, and J. Nocedal,
"A Trust Region Method Based on Interior Point Techniques for
Nonlinear Programming," *Mathematical Programming*,
Vol 89, No. 1, pp. 149–185, 2000.

[41] Byrd, R.H., Mary E. Hribar, and Jorge Nocedal,
"An Interior Point Algorithm for Large-Scale Nonlinear Programming," *SIAM
Journal on Optimization*, Vol 9, No. 4, pp. 877–900,
1999.

[42] Byrd, R.H., R.B. Schnabel, and G.A. Shultz,
"Approximate Solution of the Trust Region Problem by Minimization
over Two-Dimensional Subspaces," *Mathematical Programming*,
Vol. 40, pp 247–263, 1988.

[43] Coleman, T.F. and Y. Li, "On the Convergence
of Reflective Newton Methods for Large-Scale Nonlinear Minimization
Subject to Bounds," *Mathematical Programming*,
Vol. 67, Number 2, pp 189–224, 1994.

[44] Coleman, T.F. and Y. Li, "An Interior,
Trust Region Approach for Nonlinear Minimization Subject to Bounds," *SIAM
Journal on Optimization*, Vol. 6, pp 418–445, 1996.

[45] Coleman, T.F. and Y. Li, "A Reflective
Newton Method for Minimizing a Quadratic Function Subject to Bounds
on some of the Variables," *SIAM Journal on Optimization*,
Vol. 6, Number 4, pp 1040–1058, 1996.

[46] Coleman, T.F. and A. Verma, "A Preconditioned
Conjugate Gradient Approach to Linear Equality Constrained Minimization," *Computational
Optimization and Applications*, Vol. 20, No. 1, pp. 61–72,
2001.

[47] Mehrotra, S., "On the Implementation
of a Primal-Dual Interior Point Method," *SIAM Journal
on Optimization*, Vol. 2, pp 575–601, 1992.

[48] Moré, J.J. and D.C. Sorensen, "Computing
a Trust Region Step," *SIAM Journal on Scientific
and Statistical Computing*, Vol. 3, pp 553–572,
1983.

[49] Sorensen, D.C., "Minimization of a Large Scale Quadratic Function Subject to an Ellipsoidal Constraint," Department of Computational and Applied Mathematics, Rice University, Technical Report TR94-27, 1994.

[50] Steihaug, T., "The Conjugate Gradient
Method and Trust Regions in Large Scale Optimization," *SIAM
Journal on Numerical Analysis*, Vol. 20, pp 626–637,
1983.

[51] Waltz, R. A. , J. L. Morales, J. Nocedal,
and D. Orban, "An interior algorithm for nonlinear optimization
that combines line search and trust region steps," *Mathematical
Programming*, Vol 107, No. 3, pp. 391–408, 2006.

[52] Zhang, Y., "Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment," Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, Technical Report TR96-01, July, 1995.

[53] Hairer, E., S. P. Norsett, and G. Wanner, *Solving
Ordinary Differential Equations I - Nonstiff Problems*,
Springer-Verlag, pp. 183–184.

[54] Chvatal, Vasek, *Linear Programming*,
W. H. Freeman and Company, 1983.

[55] Bixby, Robert E., "Implementing the Simplex Method: The Initial Basis," ORSA Journal on Computing, Vol. 4, No. 3, 1992.

[56] Andersen, Erling D. and Knud D. Andersen, "Presolving in Linear Programming," Mathematical Programming, Vol. 71, pp. 221–245, 1995.

[57] Lagarias, J. C., J. A. Reeds, M. H. Wright,
and P. E. Wright, "Convergence Properties of the Nelder-Mead
Simplex Method in Low Dimensions," *SIAM Journal
of Optimization*, Vol. 9, Number 1, pp. 112–147,
1998.

[58] Dolan, Elizabeth D. , Jorge J. Moré and Todd S. Munson, "Benchmarking Optimization Software with COPS 3.0," Argonne National Laboratory Technical Report ANL/MCS-TM-273, February 2004.

[59] Applegate, D. L., R. E. Bixby, V. Chvátal
and W. J. Cook, *The Traveling Salesman Problem: A Computational
Study*, Princeton University Press, 2007.

[60] Spellucci, P., "A new technique for
inconsistent QP problems in the SQP method," *Journal
of Mathematical Methods of Operations Research*, Volume
47, Number 3, pp. 355–400, October 1998.

[61] Tone, K., "Revisions of constraint
approximations in the successive QP method for nonlinear programming
problems," *Journal of Mathematical Programming*,
Volume 26, Number 2, pp. 144–152, June 1983.

[62] Gondzio, J. "Multiple centrality
corrections in a primal dual method for linear programming." *Computational
Optimization and Applications*, Volume 6, Number 2, pp.
137–156, 1996.

[63] Gould, N. and P. L. Toint. "Preprocessing
for quadratic programming." *Math. Programming*,
Series B, Vol. 100, pp. 95–132, 2004.

[64] Schittkowski, K., "More Test Examples
for Nonlinear Programming Codes," *Lecture Notes
in Economics and Mathematical Systems*, Number 282, Springer,
p. 45, 1987.

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