An algorithm for composite nonsmooth optimization problems (original) (raw)

References

  1. Clarke, F. H.,Generalized Gradients and Applications, Transactions of the American Mathematical Society, Vol. 205, pp. 247–262, 1975.
    Google Scholar
  2. Lemarechal, C.,Bundle Methods in Nonsmooth Optimization, Nonsmooth Optimization, Edited by C. Lemarechal and R. Mifflin, Pergamon Press, Oxford, England, pp. 71–78, 1978.
    Google Scholar
  3. Fletcher, R.,Practical Methods of Optimization, Vol. 2, Constrained Optimization, John Wiley and Sons, New York, New York, 1981.
    Google Scholar
  4. Womersley, R. S.,Numerical Methods for Structured Problems in Nonsmooth Optimization, University of Dundee, PhD Thesis, 1981.
  5. Womersley, R. S.,Optimality Conditions for Piecewise Smooth Functions, Mathematical Programming Study No. 17, pp. 13–27, 1982.
  6. Powell, M. J. D.,The Convergence of Variable Metric Methods for Nonlinearly Constrained Optimization Calculations, Nonlinear Programming 3, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, London, England, 1978.
    Google Scholar
  7. Charalambous, C., andConn, A. R.,An Efficient Method to Solve the Minimax Problem Directly, SIAM Journal on Numerical Analysis, Vol. 15, pp. 162–187, 1978.
    Google Scholar
  8. Conn, A. R.,An Efficient Second-Order Method to Solve the Constrained Minimax Problem, University of Waterloo, Department of Combinatorics and Optimization, Report CORR-79-5, 1979.
  9. Fletcher, R.,A Model Algorithm for Composite Nondifferentiable Optimization Problems, Mathematical Programming Study No. 10, pp. 67–76, 1982.
  10. Hald, J., andMadsen, K.,Combined LP and Quasi-Newton Methods for Minimax Optimization, Mathematical Programming, Vol. 20, pp. 49–62, 1981.
    Google Scholar
  11. Han, S. P.,Variable Metric Methods for Minimizing a Class of Nondifferentiable Functions, Mathematical Programming, Vol. 20, pp. 1–13, 1981.
    Google Scholar
  12. Murray, W., andOverton, M. L.,A Projected Lagrangian Algorithm for Nonlinear Minimax Optimization, SIAM Journal on Scientific and Statistical Computing, Vol. 1, pp. 345–370, 1980.
    Google Scholar
  13. Fletcher, R.,Practical Methods of Optimization, Vol. 1, Unconstrained Optimization, John Wiley and Sons, New York, New York, 1980.
    Google Scholar
  14. Wolfe, P.,Sufficient Minimization of Piecewise Linear Univariate Functions, Nonsmooth Optimization, Edited by C. Lemarechal and R. Mifflin, Pergamon Press, Oxford, England, 1978.
    Google Scholar
  15. Murray, W., andOverton, M. L.,Steplength Algorithms for Minimizing a Class of Nondifferentiable Functions, Computing, Vol. 23, pp. 309–331, 1979.
    Google Scholar
  16. Fletcher, R.,Numerical Experiments with an Exact L 1-Penalty Function, Nonlinear Programming 4, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, New York, New York, pp. 99–129, 1981.
    Google Scholar
  17. Pshenichnyi, V. N.,Nonsmooth Optimization and Nonlinear Programming, Nonsmooth Optimization, Edited by C. Lemarechal and R. Mifflin, Pergamon Press, Oxford, England, 1978.
    Google Scholar
  18. Gill, P. E., andMurray, W.,The Computation of Lagrange Multiplier Estimates for Constrained Optimization, Mathematical Programming, Vol. 17, pp. 32–60, 1979.
    Google Scholar
  19. Coleman, T. F., andConn, R. R.,Nonlinear Programming via an Exact Penalty Function: Asymptotic Analysis, Mathematical Programming, Vol. 24, pp. 123–136, 1982.
    Google Scholar
  20. Coleman, T. F., andConn, A. R.,Nonlinear Programming via an Exact Penalty Function: Global Analysis, Mathematical Programming, Vol. 24, pp. 137–161, 1982.
    Google Scholar
  21. Gill, P. E., andMurray, W.,Numerically Stable Methods for Quadratic Programming, Mathematical Programming, Vol. 14, pp. 349–372, 1978.
    Google Scholar
  22. Powell, M. J. D.,A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, Numerical Analysis, Dundee 1977, Edited by G. A. Watson, Springer-Verlag, Berlin, Germany, pp. 144–157, 1977.
    Google Scholar
  23. Powell, M. J. D.,A Hybrid Method for Nonlinear Equations, Numerical Methods for Nonlinear Equations, Edited by P. Rabinowitz, Gordon and Breach, London, England, 1970.
    Google Scholar
  24. Mayne, D. Q.,On the Use of Exact Penalty Functions to Determine Steplength in Optimization Algorithms, Numerical Analysis, Dundee 1979, Edited by G. A. Watson, Springer-Verlag, Berlin, Germany, 1980.
    Google Scholar
  25. Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., andPedersen, H. C.,The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization, Mathematical Programming Study No. 16, pp. 1–17, 1982.
  26. Charalambous, C., andBandler, J. W.,Nonlinear Minimax Optimization as a Sequence of Least pth Optimization with Finite Values of p, International Journal of Systems Science, Vol. 7, pp. 377–394, 1976.
    Google Scholar
  27. Powell, M. J. D.,Algorithms for Nonlinear Constraints That Use Lagrangian Functions, Mathematical Programming, Vol. 14, pp. 224–248, 1978.
    Google Scholar
  28. Rosenbrock, H. H.,An Automatic Method for Finding the Greatest or Least Value of a Function, Computer Journal, Vol. 3, pp. 175–184, 1960.
    Google Scholar
  29. Barrodale, I., Powell, M. J. D., andRoberts, E. D. K.,The Differential Correction Algorithm for Rational L ∞-Approximation, SIAM Journal on Numerical Analysis, Vol. 7, pp. 493–504, 1972.
    Google Scholar
  30. Rosen, J. B., andSuzuki, S.,Construction of Nonlinear Programming Test Problems, Communications of the Association of Computing Machinery, Vol. 8, p. 113, 1965.
    Google Scholar
  31. Colville, A. R.,A Comparative Study on Nonlinear Programming Codes, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, Report No. 320-2949, 1968.
    Google Scholar
  32. Freudenstein, F., andRoth, B.,Numerical Solution of Systems of Nonlinear Equations, Journal of the Association of Computing Machinery, Vol. 10, pp. 550–556, 1963.
    Google Scholar
  33. Fletcher, R.,An Ideal Penalty Function for Constrained Optimization, Journal of the Institute of Mathematics and Its Applications, Vol. 15, pp. 319–342, 1975.
    Google Scholar
  34. Coleman, T. F., andSorensen, D. C.,A Note on the Computation of an Orthogonal Basis for the Null Space of a Matrix, Mathematical Programming, Vol. 29, pp. 234–242, 1984.
    Google Scholar
  35. Fletcher, R.,Second-Order Corrections for Nondifferentiable Optimization, Numerical Analysis, Dundee 1981, Edited by G. A. Watson, Springer-Verlag, Berlin, Germany, pp. 85–114, 1982.
    Google Scholar

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