Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

作者: A. A. Brown , M. C. Bartholomew-Biggs

DOI: 10.1007/BF00941054

关键词: Constrained optimizationMathematical optimizationSystems theoryOdeMathematicsFundamental Resolution EquationTheory of computationMinificationDifferential equationOrdinary differential equation

摘要: … Methods of this type for optimization (and for the related problem of solving sets of nonlinear equations) have been proposed by a number … numerical solution to the scalar test equation …

参考文章(15)
M. J. D Powell, Nonlinear optimization 1981 noop. ,(1982)
J.A. Snyman, A new and dynamic method for unconstrained minimization Applied Mathematical Modelling. ,vol. 6, pp. 449- 462 ,(1982) , 10.1016/S0307-904X(82)80007-3
M. C. BIGGS, Minimization Algorithms Making Use of Non-quadratic Properties of the Objective Function Ima Journal of Applied Mathematics. ,vol. 8, pp. 315- 327 ,(1971) , 10.1093/IMAMAT/8.3.315
C.A Botsaris, A curvilinear optimization method based upon iterative estimation of the eigensystem of the Hessian matrix Journal of Mathematical Analysis and Applications. ,vol. 63, pp. 396- 411 ,(1978) , 10.1016/0022-247X(78)90085-9
C.A Botsaris, A class of methods for unconstrained minimization based on stable numerical integration techniques Journal of Mathematical Analysis and Applications. ,vol. 63, pp. 729- 749 ,(1978) , 10.1016/0022-247X(78)90068-9
C.A Botsaris, D.H Jacobson, A Newton-type curvilinear search method for optimization Journal of Mathematical Analysis and Applications. ,vol. 54, pp. 217- 229 ,(1976) , 10.1016/0022-247X(76)90246-8
Sandro Incerti, Valerio Parisi, Francesco Zirilli, A New Method for Solving Nonlinear Simultaneous Equations SIAM Journal on Numerical Analysis. ,vol. 16, pp. 779- 789 ,(1979) , 10.1137/0716057
Filippo Aluffi-Pentini, Valerio Parisi, Francesco Zirilli, Algorithm 617: DAFNE: a differential-equations algorithm for nonlinear equations ACM Transactions on Mathematical Software. ,vol. 10, pp. 317- 324 ,(1984) , 10.1145/1271.1632
C.A Botsaris, Differential gradient methods Journal of Mathematical Analysis and Applications. ,vol. 63, pp. 177- 198 ,(1978) , 10.1016/0022-247X(78)90114-2