A modular system of algorithms for unconstrained minimization
ACM Transactions on Mathematical Software (TOMS)
A new modified Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Derivative and secant tensor methods for unconstrained optimization
Derivative and secant tensor methods for unconstrained optimization
EFCOSS: An interactive environment facilitating optimal experimental design
ACM Transactions on Mathematical Software (TOMS)
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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.