Algorithm 738
Algorithm 738: a software package for unconstrained optimization using tensor methods. This paper describes a software package for finding the unconstrained minimizer of a nonlinear function of n variables. The package is intended for problems where n is not too large—say, n 100—so that the cost of storing one n × n matrix, and factoring it at each iteration, is acceptable. The software allows the user to choose between a recently developed “tensor method” for unconstrained optimization and an analogous standard method based on a quadratic model. The tensor method bases each iteration on a specially constructed fourth-order model of the objective function not significantly more expensive to form, store, or solve than the standard quadratic model. In our experience, the tensor method requires significantly fewer iterations and function evaluations to solve most unconstrained optimization problems than standard methods based on quadratic models, and also solves a somewhat wider range of problems. For these reasons, it may be a useful addition to numerical software libraries.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
Sorted by year (- Liu, Zexian; Liu, Hongwei: An efficient gradient method with approximately optimal stepsize based on tensor model for unconstrained optimization (2019)
- Wang, Ting; Liu, Zexian; Liu, Hongwei: A new subspace minimization conjugate gradient method based on tensor model for unconstrained optimization (2019)
- Beebe, Nelson H. F.: The mathematical-function computation handbook. Programming using the MathCW portable software library (2017)
- Öztoprak, Figen; Birbil, Ş. İlker: A symmetric rank-one quasi-Newton line-search method using negative curvature directions (2011)
- Rasch, Arno; Bücker, H. Martin: EFCOSS: an interactive environment facilitating optimal experimental design (2010)
- Doyle, Francis J. III; Pearson, Ronald K.; Ogunnaike, Babatunde A.: Identification and control using Volterra models (2001)
- Maner, Bryon R.; Doyle, Francis J. III.; Ogunnaike, Babatunde A.; Pearson, Ronald K.: Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models (1996)
- Bratley, Paul; Fox, Bennett L.; Niederreiter, Harald: Algorithm 738: Programs to generate Niederreiter’s low-discrepancy sequences (1994)