TaoAddTerm#

Add a term to the objective function. If Tao is empty, term will be the objective of Tao.

Synopsis#

#include "petsctao.h" 
PetscErrorCode TaoAddTerm(Tao tao, const char prefix[], PetscReal scale, TaoTerm term, Vec params, Mat map)

Collective

Input Parameters#

tao - a Tao solver context
prefix - the prefix used for configuring the new term (if NULL, the index of the term will be used as a prefix, e.g. “0_”, “1_”, etc.)
scale - scaling coefficient for the new term
term - the real-valued function defining the new term
params - (optional) parameters for the new term. It is up to each implementation of TaoTerm to determine how it behaves when parameters are omitted.
map - (optional) a map from the tao solution space to the term solution space; if NULL the map is assumed to be the identity

Notes#

If the objective function was \(f(x)\), after calling TaoAddTerm() it becomes \(f(x) + \alpha g(Ax; p)\), where \(\alpha\) is the scale, \(g\) is the term, \(A\) is the (optional) map, and \(p\) are the (optional) params of \(g\).

The map \(A\) transforms the Tao solution vector into the term’s solution space. For example, if the Tao solution vector is \(x \in \mathbb{R}^n\) and the mapping matrix is \(A \in \mathbb{R}^{m \times n}\), then the term evaluates \(g(Ax; p)\) with \(Ax \in \mathbb{R}^m\). The term’s solution space is therefore \(\mathbb{R}^m\). If the map is NULL, the identity is used and the term’s solution space must match the Tao solution space. Tao automatically applies the chain rule for gradients (\(A^T \nabla g\)) and Hessians (\(A^T \nabla^2 g \, A\)) with respect to \(x\).

The params \(p\) are fixed data that are not optimized over. Some TaoTermTypes require the parameter space to be related to the term’s solution space (e.g., the same size); when a mapping matrix \(A\) is used, the parameter space may depend on either the row or column space of \(A\). See the documentation for each TaoTermType.

Currently, TaoAddTerm() does not support bounded Newton solvers (TAOBNK,TAOBNLS,TAOBNTL,TAOBNTR,and TAOBQNK)

Level#

beginner

Location#

src/tao/interface/taosolver.c

Examples#

src/tao/unconstrained/tutorials/elastic_net_regularization.c
src/tao/unconstrained/tutorials/rosenbrock1_taoterm.c

Index of all Tao routines
Table of Contents for all manual pages
Index of all manual pages