Optimization.Constrained.Penalty

Building the problem

data Opt f a

Opt d f gs hs is a Lagrangian optimization problem with objective f equality (g(x) == 0) constraints gs and less-than (h(x) < 0) constraints hs

newtype FU f a

Constructors

FU

Fields

• runFU :: forall s. Mode s => f (AD s a) -> AD s a

optimize :: (forall s. Mode s => f (AD s a) -> AD s a) -> Opt f a

constrainEQ :: (forall s. Mode s => f (AD s a) -> AD s a) -> Opt f a -> Opt f a

constrainLT :: (forall s. Mode s => f (AD s a) -> AD s a) -> Opt f a -> Opt f a

constrainGT :: Num a => (forall s. Mode s => f (AD s a) -> AD s a) -> Opt f a -> Opt f a

Optimizing the problem

minimize

Arguments

:: (Functor f, RealFrac a, Ord a, g ~ V)

=> (FU f a -> f a -> [f a])

Primal minimizer

-> Opt f a

The optimization problem of interest

-> a

The penalty increase factor

-> f a

The primal starting value

-> g a

The dual starting value

-> [f a]

Optimizing iterates

Minimize the given constrained optimization problem This is a basic penalty method approach

maximize

Arguments

:: (Functor f, RealFrac a, Ord a, g ~ V)

=> (FU f a -> f a -> [f a])

Primal minimizer

-> Opt f a

The optimization problem of interest

-> a

The penalty increase factor

-> f a

The primal starting value

-> g a

The dual starting value

-> [f a]

Optimizing iterates

Maximize the given constrained optimization problem

Finding the Lagrangian

lagrangian :: Num a => Opt f a -> forall s. Mode s => f (AD s a) -> V (AD s a) -> AD s a

The Lagrangian for the given constrained optimization