TSSetCostHessianProducts#

Sets the initial value of the Hessian-vector products of the cost function w.r.t. initial values and w.r.t. the problem parameters for use by the TS adjoint routines.

Synopsis#

#include <petscts.h>  
PetscErrorCode TSSetCostHessianProducts(TS ts, PetscInt numcost, Vec *lambda2, Vec *mu2, Vec dir)

Logically Collective

Input Parameters#

ts - the TS context obtained from TSCreate()
numcost - number of cost functions
lambda2 - Hessian-vector product with respect to the initial condition variables, the dimension and parallel layout of these vectors is the same as the ODE solution vector
mu2 - Hessian-vector product with respect to the parameters, the number of entries in these vectors is the same as the number of parameters
dir - the direction vector that are multiplied with the Hessian of the cost functions

Notes#

Hessian of the cost function is completely different from Hessian of the ODE/DAE system

For second-order adjoint, one needs to call this function and then TSAdjointSetForward() before TSSolve().

After TSAdjointSolve() is called, the lambda2 and the mu2 will contain the computed second-order adjoint sensitivities, and can be used to produce Hessian-vector product (not the full Hessian matrix). Users must provide a direction vector; it is usually generated by an optimization solver.

Passing NULL for lambda2 disables the second-order calculation.

Level#

beginner

Location#

src/ts/interface/sensitivity/tssen.c

Examples#

src/ts/tutorials/ex20opt_p.c
src/ts/tutorials/ex20opt_ic.c

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