# 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#

number of cost functions**numcost -**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**lambda2 -**Hessian-vector product with respect to the parameters, the number of entries in these vectors is the same as the number of parameters**mu2 -**the direction vector that are multiplied with the Hessian of the cost functions**dir -**

## 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.

## See Also#

TS: Scalable ODE and DAE Solvers, `TS`

, `TSAdjointSolve()`

, `TSAdjointSetForward()`

## Level#

beginner

## Location#

## Examples#

src/ts/tutorials/ex20opt_ic.c

src/ts/tutorials/ex20opt_p.c

Index of all Sensitivity routines

Table of Contents for all manual pages

Index of all manual pages