petsc-3.14.5 2021-03-03
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# 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 TSAdjoint routines.

### Synopsis

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

Logically Collective on TS

### 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 lamba2 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

TSAdjointSetForward()

### Level

beginner

### Location

src/ts/interface/sensitivity/tssen.c

### Examples

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