Bibliography for the Steepest Descent - Gradient Search

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  1. A steepest descent algorithm for circularity evaluation
    Zhu, L. M.; Ding, H.; Xiong, Y. L.
    Computer Aided Design, 2003, vol. 35, no. 3, pp. 255-265, Ingenta.  
  2. Parallel Implementation of the Steepest Descent Fast Multipole Method (SDFMM) on a Beowulf Cluster for Subsurface Sensing Applications
    Jiang, D.; Meleis, W.; El-Shenawee, M.; Mizan, E.; Ashouei, M.; Rappaport, C.
    IEEE Microwave and Wireless Components Letters, 2002, vol. 12, no. 1, pp. 24-26, Ingenta.  
  3. Monte Carlo simulations of electromagnetic wave scattering from a random rough surface with three-dimensional penetrable buried object: mine detection application using the steepest-descent fast multipole method
    El-Shenawee, M.; Rappaport, C.; Silevitch, M.
    Journal- Optical Society of America A, 2001, vol. 18, no. 12, pp. 3077-3084, Ingenta.  
  4. Steepest descent methods for multicriteria optimization.    
    Fliege, Jörg; Svaiter, Benar Fux    
    Math. Methods Oper. Res. 51 (2000), no. 3, 479--494, MathSciNet.  
  5. Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence.    
    Cominetti, R.; Alemany, O.    
    Trans. Amer. Math. Soc. 351 (1999), no. 12, 4847--4860, MathSciNet.  
  6. An enhanced response surface methodology (RSM) algorithm using gradient deflection and second-order search strategies.    
    Joshi, Shirish; Sherali, Hanif D.; Tew, Jeffrey D.    
    Comput. Oper. Res. 25 (1998), no. 7-8, 531--541, MathSciNet.  
  7. The origin of the method of steepest descent.    
    Petrova, Svetlana S.; Solovprime ev, Alexander D.    
    Historia Math. 24 (1997), no. 4, 361--375, MathSciNet.  
  8. Use of steepest descent for certain quadratic constraints.    
    Kim, Keehwan    
    Far East J. Math. Sci. 4 (1996), no. 3, 443--451, MathSciNet.  
  9. Full Convergence of the Steepest Descent Method with Inexact Line Searches.
    Burachik, R.; Drummond, L.M.G.; Svaiter, B.F.
    Optimization, 1995, vol. 32, no. 2, pp. 137--146, Ingenta.  
  10. Steepest Descent Algorithms for Neural Network Controllers and Filters.
    Piche, S.W.
    IEEE transactions on neural networks, 1994, vol. 5, no. 2, pp. 198, Ingenta.  
  11. A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation  
    P. Deift, X. Zhou  
    The Annals of Mathematics, 2nd Ser., Vol. 137, No. 2. (Mar., 1993), pp. 295-368, Jstor.  
  12. On the Identification Property of a Projected Gradient Method  
    P. L. De Angelis; G. Toraldo  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1483-1497, Jstor.  
  13. An interactive multi-objective gradient search.    
    Ringuest, Jeffrey L.; Gulledge, Thomas R.    
    Oper. Res. Lett. 12 (1992), no. 1, 53--58, MathSciNet.  
  14. Maximum Length of Steepest Descent Curves for Quasi-Convex Functions.
    Manselli, Paolo
    Geometriae dedicata, 1991, vol. 38, no. 2, pp. 211, Ingenta.  
  15. A trajectory algorithm based on the gradient method. I. The search on the quasioptimal trajectories.    
    Sturua, E. G.; Zavriev, S. K.     
    2nd IIASA Workshop on Global Optimization (Sopron, 1990). J. Global Optim. 1 (1991), no. 4, 375--388, MathSciNet.  
  16. The steepest descent gravitational method for linear programming.
    Chang, S.Y.; Murty, K.G.
    Discrete applied mathematics and combinatorial operations research, 1989, vol. 25, no. 3, pp. 211, Ingenta.  
  17. Nonorthogonal Analysis of Variance Using Gradient Methods (in Theory and Methods)  
    Mortaza Jamshidian; Robert I. Jennrich  
    Journal of the American Statistical Association, Vol. 83, No. 402. (Jun., 1988), pp. 483-489, Jstor.  
  18. A numerical comparison of conjugate gradient-like methods.
    Langtangen, Hans Petter; Tveito, Aslak
    Comm. Appl. Numer. Methods 4 (1988), no. 6, 793--798, MathSciNet.  
  19. A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation  
    Avi Vardi  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 3. (Jun., 1985), pp. 575-591, Jstor.  
  20. A numerical study of various algorithms related to the preconditioned conjugate gradient method.
    Jackson, C. P.; Robinson, P. C.
    Internat. J. Numer. Methods Engrg. 21 (1985), no. 7, 1315--1338, MathSciNet.  
  21. Newton-Type Minimization Via the Lanczos Method  
    Stephen G. Nash  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 770-788, Jstor.  
  22. Gradient Method for Nondensely Defined Closed Unbounded Linear Operators  
    Sung J. Lee; M. Zuhair Nashed  
    Proceedings of the American Mathematical Society, Vol. 88, No. 3. (Jul., 1983), pp. 429-435, Jstor.  
  23. An Efficient Method to Solve the Minimax Problem Directly  
    C. Charalambous; A. R. Conn  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 1. (Feb., 1978), pp. 162-187, Jstor.  
  24. A steepest-descent method for optimization of mechanical systems.
    Haug, E. J.; Arora, J. S.; Matsui, K.
    J. Optimization Theory Appl. 19 (1976), no. 3, 401--424, MathSciNet.  
  25. An Historical Survey of Computational Methods in Optimal Control  
    E. Polak  
    SIAM Review, Vol. 15, No. 2, Part 2: Anniversary Supplement. (Apr., 1973), pp. 553-584, Jstor.  
  26. Steepest Descent for Singular Linear Operator Equations  
    M. Z. Nashed  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 3. (Sep., 1970), pp. 358-362, Jstor.  
  27. Conditioning of Quasi-Newton Methods for Function Minimization  
    D. F. Shanno  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 647-656, Jstor.  
  28. Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems  
    Yonathan Bard  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 1. (Mar., 1970), pp. 157-186, Jstor.  
  29. Variational approach to the gradient method: Theory and numerical experiments.
    Miele, Angelo
    1969 Computing Methods in Optimization Problems (Second Internat. Conf., San Remo, 1968) pp. 143--157 Springer, Berlin, MathSciNet.  
  30. Two Algorithms Related to the Method of Steepest Descent  
    T. M. Whitney, R. K. Meany  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 1. (Mar., 1967), pp. 109-118, Jstor.  
  31. On the Relative Efficiencies of Gradient Methods  
    John Greenstadt  
    Mathematics of Computation, Vol. 21, No. 99. (Jul., 1967), pp. 360-367, Jstor.  
  32. A Ricocheting Gradient Method for Nonlinear Optimization  
    J. L. Greenstadt  
    SIAM Journal on Applied Mathematics, Vol. 14, No. 3. (May, 1966), pp. 429-445, Jstor.  
  33. Maximization by Quadratic Hill-Climbing  
    Stephen M. Goldfeld; Richard E. Quandt; Hale F. Trotter  
    Econometrica, Vol. 34, No. 3. (Jul., 1966), pp. 541-551, Jstor.  
  34. The Circles of Curvature of the Curves of Steepest Descent of Green's Function  
    J. L. Walsh  
    The American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), pp. 323-329, Jstor.  
  35. On the Optimum Gradient Method for Systems of Linear Equations  
    M. Marcus  
    Proceedings of the American Mathematical Society, Vol. 7, No. 1. (Feb., 1956), pp. 77-81, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004