Abstract
A brief survey is given of the main ideas that are used in current optimization algorithms. Attention is given to the purpose of each technique instead of to its details. It is believed that all the techniques that are mentioned are important to the development of useful algorithms.
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References
Bertsekas, D.P. (1982), “Constrained optimization and Lagrange multiplier methods”, Academic Press, New York.
Biggs, M.C. (1975), “Constrained minimization using recursive quadratic programming: some alternative subproblem formulations”, in “Towards global optimization”, eds. L.C.W. Dixon and G.P. Szegö, North-Holland Publishing Co., Amsterdam.
Boggs, P.T. and Tolle, J.W. (1980), “Augmented Lagrangians which are quadratic in the multiplier”, J. Optim. Theory Appl., 31, pp. 17–26.
Buckley, A.G. (1975), “An alternate implementation of Goldfarb’s minimization algorithm”, Math. Programming, 8, pp. 207–231.
Buckley, A.G. (1982), “Conjugate gradient methods”, in “Nonlinear optimization 1981”, ed. M.J.D. Powell, Academic Press, London.
Davidon, W.C. (1980), “Conic approximations and collinear scalings for optimizers”, SIAM J. Numer. Anal., 17, pp. 268–281.
Dennis, J.E. and More, J.J. (1977), “Quasi-Newton methods, motivation and theory”, SIAM Rev., 19, pp. 46–89.
Dennis, J.E. and Schnabel, R.B. (1979), “Least change secant updates for quasi-Newton methods”, SIAM Rev., 21, pp. 443–459.
Di Pillo, G. and Grippo, L. (1979), “A new class of augmented Lagrangians in nonlinear.programming”, SIAM J. Control Optim., 17, pp. 618–628.
Dixon, L.C.W. (1972), “Nonlinear optimization”, English Universities Press, London.
Fiacco, A.V. and McCormick, G.P. (1968), “Nonlinear programming: sequential unconstrained minimization techniques”, John Wiley and Sons, New York.
Fletcher, R. (1972), “An algorithm for solving linearly constrained optimization problems”, Math. Programming, 2, pp. 133–165.
Fletcher, R. (1973), “An exact penalty function for nonlinear programming with inequalities”, Math. Programming, 5, pp. 129–150.
Fletcher, R. (1975), “An ideal penalty function for constrained optimization problems”, in “Nonlinear programming 2”, eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Academic Press, New York.
Fletcher, R. (1980), “Practical methods of optimization, vol. 1: unconstrained optimization”, John Wiley and Sons, Chichester.
Fletcher, R. (1981), “Nonlinear experiments with an exact L1 penalty function method“, in ”Nonlinear programming 4”, eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Academic Press, New York.
Fletcher, R. (1982), “Methods for nonlinear constraints”, in “Nonlinear optimization 1981”, ed. M.J.D. Powell, Academic Press, London.
Gill, P.E. and Murray, W. (1977), “Linearly constrained problems including linear and quadratic programming”, in “The state of the art in numerical analysis”, ed. D.A.H. Jacobs, Academic Press, London.
Griewank, A. and Toint, Ph.L. (1982), “On the unconstrained optimization of partially separable functions”, in “Nonlinear optimization 1981”, ed. M.J.D. Powell, Academic Press, London.
Han, S.P. (1977), “A globally convergent method for nonlinear programming”, J. Optim. Theory Appl., 22, pp. 297–309.
Hock, W. and Schittkowski, K. (1981), “Test examples for nonlinear programming codes: lecture notes in economics and mathematical systems 187”, Springer Verlag, Berlin.
Lasdon, L.S. (1982), “Reduced gradient methods”, in “Nonlinear optimization 1981”, ed. M.J.D. Powell, Academic Press, London.
Murtagh, B.A. and Saunders, M.A. (1978), “Large scale linearly constrained optimization”, Math. Programming, 14, pp. 41–72.
Osborne, M.R. and Watson, G.A. (1971), “On an algorithm for discrete nonlinear Li approximation”, Comput. J., 14, pp. 184–188.
Pietrzykowski, T. (1969), “An exact potential method for constrained maxima”, SIAM J. Numer. Anal., 6, pp. 294–304.
Polak, E. (1971), “Computational methods in optimization - a unified approach”, Academic Press, New York.
Powell, M.J.D. (1974), “Introduction to constrained optimization”, in “Numerical methods for constrained optimization”, eds. P.E. Gill and W. Murray, Academic Press, London.
Powell, M.J.D. (1978), “A fast algorithm for nonlinearly constrained optimization calculations”, in “Numerical analysis, Dundee 1977, lecture notes in mathematics 630”, ed. G.A. Watson, Springer Verlag, Berlin.
Powell, M.J.D. (1978), “The convergence of variable metric methods for nonlinearly constrained optimization calculations”, in “Nonlinear programming 3”, eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Academic Press, New York.
Powell, M.J.D. (1978), “Algorithms for nonlinear constraints that use Lagrangian functions”, Math. Programming, 14, pp. 224–248.
Powell, M.J.D. (1982), “Extensions to subroutine VF02AD”, to be published in “Proceedings of the tenth IFIP conference on optimization techniques”, Springer-Verlag.
Powell, M.J.D. (1982), ed. “Nonlinear optimization 1981”, Academic Press, London.
Sorensen, D.C. (1982), “Trust region methods for unconstrained minimization”, in “Nonlinear optimization 1981”, ed. M.J.D. Powell, Academic Press, London.
Toint, Ph.L. (1981), “Towards an efficient sparsity exploiting Newton method for minimization”, in “Sparse matrices and their uses”, ed. I. Duff, Academic Press, London.
Wilson, R.B. (1963), “A simplicial algorithm for concave programming”, Ph.D. thesis, Graduate School of Business Administration, Harvard University.
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Powell, M.J.D. (1982). Algorithms for Constrained and Unconstrained Optimization Calculations. In: Hazewinkel, M., Kan, A.H.G.R. (eds) Current Developments in the Interface: Economics, Econometrics, Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7933-8_26
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DOI: https://doi.org/10.1007/978-94-009-7933-8_26
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