aligator::PDALFunction< _Scalar > Struct Template Reference

Primal-dual augmented Lagrangian merit function. More...

#include <aligator/solvers/proxddp/merit-function.hpp>

Public Types
using	Scalar = _Scalar
using	StageModel = StageModelTpl<Scalar>
using	StageData = StageDataTpl<Scalar>
using	StageFunctionData = StageFunctionDataTpl<Scalar>
using	ConstraintStack = ConstraintStackTpl<Scalar>
using	Workspace = WorkspaceTpl<Scalar>
using	TrajOptProblem = TrajOptProblemTpl<Scalar>
using	TrajOptData = TrajOptDataTpl<Scalar>

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

Static Public Member Functions
static Scalar	evaluate (const Scalar mudyn, const Scalar mucstr, const TrajOptProblem &problem, const std::vector< VectorXs > &lams, const std::vector< VectorXs > &vs, Workspace &workspace)
	Compute the merit function at the trial point.
static Scalar	directionalDerivative (const Scalar mudyn, const Scalar mucstr, const TrajOptProblem &problem, const std::vector< VectorXs > &lams, const std::vector< VectorXs > &vs, Workspace &workspace)

Detailed Description

template<typename _Scalar>
struct aligator::PDALFunction< _Scalar >

Primal-dual augmented Lagrangian merit function.

The standard Powell-Hestenes-Rockafellar (PHR) augmented Lagrangian evaluates as:

\[ \calL_{\mu_k}(\bfx, \bfu, \bmlam^k) = J(\bfx, \bfu) + \mathscr{P}(\bfx,\bfu,\bmlam^k; \mu_k), \\ \mathscr{P} = \sum_{i=0}^{N-1} \frac{1}{2\mu_k} \left\| \Bigg[\begin{array}{c} \phi(x_i, u_i, x_{i+1}) + \mu p^k_i \\ \Pi_{N_\calC}(h(x_i, u_i) + \mu \nu^k_i) \end{array}\Bigg] \right\|^2 \]

where \(\lambda_i^k = (p_i^k, \nu_i^k)\) are the multipliers at time node \(i\), \(J\) is the trajectory cost functional, and \(\mathscr{P}\) is the penalty functional. The Gill-Robinson primal-dual variant

\[ \calM_{\mu_k}(\bfx, \bfu, \bmlam; \bmlam^k) = \calL_{\mu_k}(\bfx, \bfu, \bmlam^k) + \mathscr{P}_2 \]

also adds another penalty term

\[ \mathscr{P}_2 = \sum_{i=0}^{N-1} \frac{1}{2\mu_k}\left\| \Bigg[ (*) - \lambda_i \Bigg] \right\|^2 \]

where \((*)\) is the expression within the norm in \(\mathscr{P}\) above.

Some of the parameters of this function are obtained from the linked SolverProxDDPTpl<Scalar> instance.

Definition at line 47 of file merit-function.hpp.

Member Typedef Documentation

Scalar

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::Scalar = _Scalar

Definition at line 48 of file merit-function.hpp.

StageModel

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::StageModel = StageModelTpl<Scalar>

Definition at line 50 of file merit-function.hpp.

StageData

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::StageData = StageDataTpl<Scalar>

Definition at line 51 of file merit-function.hpp.

StageFunctionData

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::StageFunctionData = StageFunctionDataTpl<Scalar>

Definition at line 52 of file merit-function.hpp.

ConstraintStack

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::ConstraintStack = ConstraintStackTpl<Scalar>

Definition at line 53 of file merit-function.hpp.

Workspace

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::Workspace = WorkspaceTpl<Scalar>

Definition at line 54 of file merit-function.hpp.

TrajOptProblem

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::TrajOptProblem = TrajOptProblemTpl<Scalar>

Definition at line 55 of file merit-function.hpp.

TrajOptData

template<typename _Scalar >

using aligator::PDALFunction< _Scalar >::TrajOptData = TrajOptDataTpl<Scalar>

Definition at line 56 of file merit-function.hpp.

Member Function Documentation

ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar >

aligator::PDALFunction< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS

(

Scalar

)

evaluate()

template<typename _Scalar >

static Scalar aligator::PDALFunction< _Scalar >::evaluate ( const Scalar mudyn, const Scalar mucstr, const TrajOptProblem & problem, const std::vector< VectorXs > & lams, const std::vector< VectorXs > & vs, Workspace & workspace )

static

Compute the merit function at the trial point.

Warning

Evaluate the problem and proximal terms first!

directionalDerivative()

template<typename _Scalar >

static Scalar aligator::PDALFunction< _Scalar >::directionalDerivative ( const Scalar mudyn, const Scalar mucstr, const TrajOptProblem & problem, const std::vector< VectorXs > & lams, const std::vector< VectorXs > & vs, Workspace & workspace )

static

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The documentation for this struct was generated from the following file:

• include/aligator/solvers/proxddp/merit-function.hpp