Optimization Toolbox

Selected Bibliography

[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]  Censor, Y., "Pareto Optimality in Multiobjective Problems, " Appl. Math. Optimiz., Vol. 4, pp 41-59, 1977.

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

[6]  Da Cunha, N.O. and E. Polak, "Constrained Minimization Under Vector-valued Criteria in Finite Dimensional Spaces," J. Math. Anal. Appl., Vol. 19, pp 103-124, 1967.

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

[8]  Dantzig, G., A. Orden, and P. Wolfe, "Generalized Simplex Method for Minimizing a Linear from Under Linear Inequality Constraints," Pacific J. Math. Vol. 5, pp 183-195.

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

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

[11]  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.

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

[13]  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.

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

[15]  Fletcher, R., "Practical Methods of Optimization," Vol. 1, Unconstrained Optimization, and Vol. 2, Constrained Optimization, John Wiley and Sons, 1980.

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

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

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

[19]  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.

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

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

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

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

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

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

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

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

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

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

[30]  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.

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

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

[33]  Nocedal, J. and S.J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer Verlag, 1999.

[34]  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.

[35]  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.

[36]  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.

[37]  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.

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

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

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

[41]  Zadeh, L.A., "Optimality and Nonscalar-valued Performance Criteria," IEEE Trans. Automat. Contr., Vol. AC-8, p. 1, 1963.

Algorithm Improvements for Goal Attainment Method

Large-Scale Algorithms