Some Possible Papers for Final CS6676 Homework


Modified Cholesky Factorization
   Schnabel and Eskow,  SIAM Journal on Scientific and Statistical Computing,
       Vol. 11, 1990, pp. 1136 - 1158 

Trust Region Methods and Analysis
   More' and Sorensen, SIAM Journal on Scientific and Statistical Computing, 
       Vol. 4, 1983, pp. 553-572  (hookstep method)
   Shultz, Schnabel, and Byrd, SIAM Journal on Numerical Analysis
       Vol. 22, 1985, pp. 47-67  (general trust region theory/methods)
   Byrd, Schnabel, and Shultz, Mathematical Programming,
       Vol. 40, 1988, pp. 247-263  (approximate hookstep method)

Secant Methods
   Byrd, Nocedal, and Yuan, SIAM Journal on Numerical Analysis,
      Vol. 24, 1987, pp. 1171-1189  (analysis of a class of secant updates)
   Khalfan, Byrd, and Schnabel, SIAM Journal on Optimization, 
      Vol. 3, 1993, pp. 1-24   (symmetric rank one update)

Large Scale Optimization
   Dembo, Eisenstat, and Steihaug, SIAM Journal on Numerical Analysis, 
       Vol. 19, 1982, pp. 400-408   (truncated Newton)
   Steihaug, SIAM Journal on Numerical Analysis, Vol. 20, 1983, pp. 626-637    
       (truncated Newton with trust region)
   Buckley and Lenir, Mathematical Programming, Vol. 27, 1985, pp. 155-175 
       (limited memory BFGS and relation to conjugate gradient)
   Nash, SIAM Journal on Scientific and Statistical Computing, 
       Vol. 6, 1985, pp. 599-616   (truncated Newton with preconditioned CG)
   Nocedal, Mathematics of Computation, Vol. 35, 1980, pp. 773-782
       (limited memory BFGS)
   Nash and Nocedal, SIAM Journal on Optimization, Vol. 1, pp. 358-372
       (limited memory BFGS vs truncated Newton)
   Griewank and Toint, Numerische Mathematik, Vol. 39, 1982, pp. 119-137
       (partially separable secant methods) 

Finite Difference Derivative Approximation
   Coleman and More', SIAM Journal on Numerical Analysis,
      Vol. 20, 1983, pp. 187-209  (sparse finite difference Jacobians)
   Coleman and More', SIAM Journal on Numerical Analysis,
      Vol. 21, 1984, pp. 243-270  (sparse finite difference Hessians)
 
Parallel Optimization
   Byrd, Schnabel, and Shultz, Mathematical Programming, 
      Vol. 42, 1988, pp. 273-306  (parallel unconstrained optimization)

Orthogonal Distance Regression
   Boggs, Byrd, and Schnabel, SIAM Journal on Scientific and Statistical Computing,
      Vol. 8, 1987,  pp. 1052-1078 

More complex models for nonlinear equations / unconstrained optimization
   Schnabel and Frank, SIAM Journal on Numerical Analysis
      Vol. 22, 1985, pp. 47-67  ("tensor methods" for nonlinear equations)
   Schnabel and Chow, SIAM Journal on Optimization,
      Vol. 1, 1991, pp. 293-315  ("tensor methods" for unconstrained optimization)
   
Best authors ever for an optimization paper
   Hart and Soul, "Quasi-Newton methods for discretized nonlinear boundary 
      value problems", IMA Journal of Applied Mathematics,
      Vol. 11, 1973, pp. 351-359