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Optimization methods in optics

  • A. K. Rigler
  • R. J. Pegis
Chapter
Part of the Topics in Applied Physics book series (TAP, volume 41)

Keywords

Objective Function Optical Design Geometric Programming Conjugate Direction Lens Design 
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References

  1. 4.1
    D.M.Himmelblau: Applied Nonlinear Programming (McGraw-Hill, New York 1972)Google Scholar
  2. 4.2
    C. L. Lawson, R. J. Hanson: Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs 1974)Google Scholar
  3. 4.3
    J. M. Ortega, W. C. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, London 1970)Google Scholar
  4. 4.4
    B.T.Polyak: J. Sov. Math. 5, 97 (1976)Google Scholar
  5. 4.5
    T.H.Jamieson: Optimization Techniques in Lens Design American Elsevier, New York 1971)Google Scholar
  6. 4.6
    E. Isaacson, H. B. Keller: Analysis of Numerical Methods (Wiley, New York, London, Sydney 1966)Google Scholar
  7. 4.7
    R. J. Donohue, B. W. Joseph: Appl. Opt. 14, 2384 (1975)Google Scholar
  8. 4.8
    N. R. Draper, H. Smith: Applied Regression Analysis (Wiley, New York, London, Sydney 1966)Google Scholar
  9. 4.9
    E. L. Stiefel: In On Numerical Approximation, ed. by R. E. Langer (University of Wisconsin Press, Madison 1959) p. 217Google Scholar
  10. 4.10
    M. R. Osborne, G. A. Watson: Comput. J. 12,63 (1969)Google Scholar
  11. 4.11
    W. E. McBride, A. K. Rigler: Comput. J. 19, 79 (1976)Google Scholar
  12. 4.12
    C. L. Lawson: “Contributions to the Theory of Linear Least Maximum Approximation”, Ph. D. Dissertation, University of California, Los Angeles (1961)Google Scholar
  13. 4.13
    B. Ekenberg: Behand. Inf. Tid. 15, 385 (1975)Google Scholar
  14. 4.14
    C. Lanczos: Applied Analysis (Prentice-Hall, Englewood Cliffs 1956)Google Scholar
  15. 4.15
    R. Mireles: J. Opt. Soc. Am. 56, 644 (1966)Google Scholar
  16. 4.16
    C.M.Lederer: In Radioactivity in Nuclear Spectroscopy, ed. by J.H.Hamilton and M. C. Manthuruthil (Gordon and Breach, New York 1972) p. 73Google Scholar
  17. 4.17
    D. C. St.Clair, A. K. Rigler: In Computer Science and Statistics: Eighth Annual Symposium on the Interface, ed. by J. W. Frane (Health Sciences Computing Facility, University of California, Los Angeles 1975)Google Scholar
  18. 4.18
    E. Delano, R.J.Pegis: In Progress in Optics VII, ed. by E. Wolf (North-Holland, Amsterdam 1969) p. 69Google Scholar
  19. 4.19
    D.P. Feder: Appl. Opt. 2, 272 (1963)Google Scholar
  20. 4.20
    E. Delano: Appl. Opt. 2, 1251 (1963)Google Scholar
  21. 4.21
    F. J. Lopez-Lopez: “The Application of the Delano yy Diagram to Optical Design”; Ph. D. Dissertation, University of Arizona, Tucson (1973)Google Scholar
  22. 4.22
    T.P. Vogl, A. K. Rigler, B. R. Canty: Appl. Opt. 10, 2513 (1971)Google Scholar
  23. 4.23
    “Inset Light Fixtures for Airport Runways and Taxiways”, Department of Transport, Canada, Spec. No. 1271 (1968)Google Scholar
  24. 4.24
    W. L. Hyde: In Recent Advances in Optimization Techniques, ed. by A. Lavi and T.P. Vogl (Wiley, New York, London, Sydney 1966) p. 1Google Scholar
  25. 4.25
    K. Levenberg: Q. Appl. Math. 2, 164 (1944)Google Scholar
  26. 4.26
    M. R. Hestenes, E. L. Stiefel: J. Res. Nat. Bur. Stds. 49, 409 (1952)Google Scholar
  27. 4.27
    W. Davidon: “Variable Metric Methods for Minimization”, A.E.C. Res. and Dev. Rept. ANL-5990, Argonne Nat. Lab., Lemont, Ill. (1959)Google Scholar
  28. 4.28
    R.Fletcher, M.J.D.Powell: Comput. J. 6, 163 (1963)Google Scholar
  29. 4.29
    D. S. Grey: J. Opt. Soc. Am. 53, 672, 677 (1963)Google Scholar
  30. 4.30
    D.P.Feder: In Recent Advances in Optimization Techniques, ed. by A.Lavi and T.P.Vogl (Wiley, New York, London, Sydney 1966) p. 5Google Scholar
  31. 4.31
    G. Hadley: Linear Programming (Addison-Wesley, Reading, Mass., Palo Alto, London 1962)Google Scholar
  32. 4.32
    R.S. Garfïnkel, G.L.Nemhauser: Integer Programming (Wiley, New York, London, Sydney 1972)Google Scholar
  33. 4.33
    H.M.Salkin: Integer Programming (Addison-Wesley, Reading; Mass., Palo Alto, London 1975)Google Scholar
  34. 4.34
    D. Tabak, B. C. Kuo: Optimal Control by Mathematical Programming (Prentice-Hall, Englewood Cliffs 1971)Google Scholar
  35. 4.35
    R.T. Rockafellar: Convex Analysis (Princeton University Press, Princeton 1969)Google Scholar
  36. 4.36
    H. W. Kuhn, A. W. Tucker: In Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability, ed. by J.Neyman (University of California Press, Berkeley 1951) p. 481Google Scholar
  37. 4.37
    R.J. Duffin, E.L.Peterson, C.Zener: Geometric Programming — Theory and Application (Wiley, New York, London, Sydney 1967)Google Scholar
  38. 4.38
    A. V. Fiacco, G. P. McCormick: Nonlinear Programming; Sequential Unconstrained Minimization Techniques (Wiley, New York, London, Sydney 1968)Google Scholar
  39. 4.39
    P.Wolfe: Econometrica 27, 382 (1959)Google Scholar
  40. 4.40
    C.Zener: Proc. Nat. Acad. Sci. 47, 537 (1961)Google Scholar
  41. 4.41
    J. E. Kelley: J. SIAM 8, 703 (1960)Google Scholar
  42. 4.42
    R. Courant: Bull. Am. Math. Soc. 49, 1 (1943)Google Scholar
  43. 4.43
    D.P. Feder: J. Opt. Soc. Am. 52, 177 (1962)Google Scholar
  44. 4.44
    D. S. Grey: In Recent Advances in Optimization Techniques, ed. by A. Lavi and T.P. Vogl (Wildy, New York, London, Sydney 1966) p. 69Google Scholar
  45. 4.45
    W. Murray: In Proc. 6th Internat. Symposium on Mathematical Programming (Princeton University Press, Princeton 1967)Google Scholar
  46. 4.46
    W.Murray: J. Opt. Th. Appl. 7, 189 (1971)Google Scholar
  47. 4.47
    L. W. Cornwell, A. K. Rigler: Appl. Opt. 11, 1659 (1972)Google Scholar
  48. 4.48
    J.L.Greenstadt: Math. Comput. 21, 360 (1967)Google Scholar
  49. 4.49
    D. W. Marquardt: J. SIAM 11, 431 (1963)Google Scholar
  50. 4.50
    D. W. Marquardt: Technometrics 12, 591 (1970)Google Scholar
  51. 4.51
    D. D. Morrison: SIAM J. Num. Anal. 5, 83 (1968)Google Scholar
  52. 4.52
    C. G. Wynne: Proc. Phys. Soc. London 73, 777 (1959)Google Scholar
  53. 4.53
    J. Meiron: J. Opt. Soc. Am. 55, 1105 (1965)Google Scholar
  54. 4.54
    D. R. Buchele: Appl. Opt. 7, 2433 (1968)Google Scholar
  55. 4.55
    D. F. Shanno: SIAM J. Num. Anal. 7, 366 (1970)Google Scholar
  56. 4.56
    A.Jones: Comput. J. 13, 301 (1970)Google Scholar
  57. 4.57
    O. N. Stavroudis: In Advances in Computers V5, ed. by F. L. Alt and M. Rubinoff (Academic Press, New York, London 1964)Google Scholar
  58. 4.58
    G. E. Forsythe: Numer. Math. 11, 57 (1968)Google Scholar
  59. 4.59
    H. Akaike: Ann. Inst. Stat. Math. Tokyo 11, 1 (1959)Google Scholar
  60. 4.60
    R. Fletcher, C. M. Reeves: Comput. J. 7, 149 (1964)Google Scholar
  61. 4.61
    H.O. Hartley: Technometrics 3, 269 (1961)Google Scholar
  62. 4.62
    N. A. Broste: “An Orthonormal Optimization Technique: Theory, Implementation, and Application”; Ph. D. Dissertation, Carnegie-Mellon University, Pittsburgh (1968)Google Scholar
  63. 4.63
    L. W. Cornwell, R. J. Pegis, A. K. Rigler, T. P. Vogl: J. Opt. Soc. Am. 63, 576 (1973)Google Scholar
  64. 4.64
    G. W. Stewart: J. Assoc. Comput. Mach. 14, 72 (1967)Google Scholar
  65. 4.65
    M.J.D.Powell: Comput. J. 7, 303 (1964)Google Scholar
  66. 4.66
    B. V. Shah, R. J. Buehler, O. Kempthorne: J. SIAM 12, 74 (1964)Google Scholar
  67. 4.67
    R. Hooke, T. A. Jeeves: J. Assoc. Comput. Mach. 8, 212 (1961)Google Scholar
  68. 4.68
    J. Weisman, C. F. Wood, L. Rivlen: In Process Control and Applied Mathematics, ed. by L. H. Krone (Am. Inst. Chem. Eng., New York 1965) p. 50Google Scholar
  69. 4.69
    H. H. Rosenbrock: Comput. J. 3, 175 (1970)Google Scholar
  70. 4.70
    M.J.Box, D.Davies, W.H.Swann: Nonlinear Optimization Techniques (Oliver and Boyd, Edinburgh 1969)Google Scholar
  71. 4.71
    L. C. W. Dixon: In Numerical Methods for Nonlinear Optimization, ed. by F. A. Lootsma (Academic Press, New York, London 1972) p. 149Google Scholar
  72. 4.72
    C.W.Carroll: Oper. Res. 9, 169 (1961)Google Scholar
  73. 4.73
    R. E. Griffith, R. A. Stewart: Manage. Sci. 7, 379 (1961)Google Scholar
  74. 4.74
    L. Cooper, D. Steinberg: Methods of Optimization (W. B. Saunders, Philadelphia, London, Toronto 1970)Google Scholar
  75. 4.75
    J. B. Rosen: J. SIAM 8, 181 (1960)Google Scholar
  76. 4.76
    J. B. Rosen: J. SIAM 9, 514 (1961)Google Scholar
  77. 4.77
    G. E. Blau, D. J. Wilde: Can. J. Chem. Eng. 47, 317 (1969)Google Scholar
  78. 4.78
    M. Avriel, R. Dembo, U.Passy: Int. J. Num. Meth. Eng. 9, 149 (1975)Google Scholar
  79. 4.79
    R. S. Dembo: GGP: A Computer Program for the Solution of Generalized Geometric Programming Problems (McMaster University, Hamilton, Ont. 1975)Google Scholar
  80. 4.80
    E. F. Beckenbach, R. Bellman: Inequalities, Ergebnisse der Mathematik, Vol. 30 (Springer, Berlin, Heidelberg, New York 1965)Google Scholar
  81. 4.81
    H. S. Carslaw: Introduction to the Theory of Fourier's Series and Integrals, 3rd ed. (Macmillan, London 1930)Google Scholar
  82. 4.82
    S. Karlin, W.J. Studden: Tchebycheff Systems with Applications in Analysis and Statistics (Interscience, New York 1966)Google Scholar
  83. 4.83
    P. W. Baumeister: J. Opt. Soc. Am. 52, 1149 (1962)Google Scholar
  84. 4.84
    J. A. Dobrowolski: Appl. Opt. 4,937 (1965)Google Scholar
  85. 4.85
    R.T.MacIntyre: Genesee Computer Center, 20 University Avenue, Rochester, New York 14605Google Scholar
  86. 4.86
    ACCOS V: Scientific Calculations, Inc. 110 Allen's Creek Road, Rochester, New York 14618Google Scholar
  87. 4.87
    National CSS, Inc., 300 Westport Avenue, Norwalk, Conn. 06851Google Scholar
  88. 4.88
    COOL: David Grey Associates, 60 Hickory Drive, Waltham, Mass. 02154Google Scholar
  89. 4.89
    ZOOM GENII: Genesee Computer Center, Inc., 20 University Avenue, Rochester, New York 14605Google Scholar
  90. 4.90
    R. E. Hopkins, H. A. Unvala: In Lens Design with Large Computers, Proceedings of the Conference, ed. by W. L. Hyde (Institute of Optics, Rochester 1967) p. 11–1Google Scholar
  91. 4.91
    R. J. Pegis, T. P. Vogl, A. K. Rigler, R. Walters: Appl. Opt. 6, 969 (1967)Google Scholar
  92. 4.92
    T.P.Vogl, L.C.Lintner, R.J.Pegis, W.M.Waldbauer, H.A.Unvala: Appl. Opt. 11, 1087 (1972)Google Scholar
  93. 4.93
    J. S. Schruben: J. Opt. Soc. Am. 62, 1498 (1972)Google Scholar
  94. 4.94
    J. S. Schruben: J. Opt. Soc. Am. 64, 55 (1974)Google Scholar
  95. 4.95
    J. A. Hankins: Unpublished Report-Computer Science Department, University of Missouri-Rolla (1976)Google Scholar
  96. 4.96
    D. F. Rogers, J. A. Adams: Mathematical Elements for Computer Graphics (McGraw-Hill, New York 1976)Google Scholar
  97. 4.97
    D. W. Epstein, P. E. Kaus, D. D. Van Ormer: “Manufacture of Color-Kinescopes”, U. S. Pat. 2,817,276, 24 Dec. 1957Google Scholar
  98. 4.98
    “Color Television”, in McGraw-Hill Encyclopedia of Science and Technology V3 (McGraw-Hill, New York 1971) p. 316Google Scholar
  99. 4.99
    R.Bloomburgh, R.Jones, J.King, J.Pietrolewicz: IEEE Trans. BTR 11, 50 (1965)Google Scholar

Bibliographic Supplement

  1. 4.100
    J. J. Dinkel, G. A. Kochenberger: Math. Prog. 15, 261–267 (1978)Google Scholar
  2. 4.101
    R. L. Armacost: “Sensitivity Analysis in Parametric Nonlinear Programming”; Ph.D. Dissertation, George Washington University (1976)Google Scholar
  3. 4.102
    J. D. Buys, R. Gonin: Math. Prog. 12, 281–284 (1977)Google Scholar
  4. 4.103
    A. V. Fiacco: Math. Prog. 10, 287–311 (1976)Google Scholar
  5. 4.104
    J.J. Dinkel, G. A. Kochenberger, S. N. Wong: Trans. Math. Software 4, 1–14 (1978)Google Scholar
  6. 4.105
    A. Buckley: Math. Prog. 15, 200–210 (1978)Google Scholar
  7. 4.106
    A. Buckley: Math. Prog. 15, 343–348 (1978)Google Scholar
  8. 4.107
    D.P.O'Leary: “Hybrid Conjugate Gradient Algorithms”; Ph.D. Dissertation, Stanford University (1975)Google Scholar
  9. 4.108
    P.T.Boggs: SIAM J. Num. Anal. 14, 830–843 (1977)Google Scholar
  10. 4.109
    C. A. Botsaris: J. Math. Anal. & Appl. 63, 729–749 (1978)Google Scholar
  11. 4.110
    J. Opt. Th. Appl. 26, Nos. 1, 2 (1978)Google Scholar
  12. 4.111
    K. Brown, M. Minkoff, K. Hillstrom, L. Nazareth, J. Pool, B. Smith: “Progress in the Development of a Modularized Package of Algorithms for Optimization Problems”, in Ref. 4.116Google Scholar
  13. 4.112
    D.C.Dilworte: Appl. Opt. 17, 3372–3375 (1978)Google Scholar
  14. 4.113
    J. Dobrowolski, D. Lowe: Appl. Opt. 17, 3039–3050 (1978)Google Scholar
  15. 4.114
    R. E. Fischer (ed.): Computer-Aided Optical Design, Proc. SPIE, Vol. 147, Bellingham, Wash. (1978)Google Scholar
  16. 4.115
    I.Powell: Appl. Opt. 17, 3361–3367 (1978)Google Scholar
  17. 4.116
    L. C. W. Dixon (ed.): Optimization in Action (Academic Press, New York 1976)Google Scholar
  18. 4.117
    L. C. Wellford (ed.): Application of Computer Methods in Engineering (University of Southern California, Los Angeles 1977)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • A. K. Rigler
  • R. J. Pegis

There are no affiliations available

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