| Safe Haskell | Safe-Inferred |
|---|
Optimization.Constrained.ProjectedSubgradient
- projSubgrad :: (Additive f, Traversable f, Metric f, Ord a, Fractional a) => StepSched f a -> (f a -> f a) -> (f a -> f a) -> (f a -> a) -> f a -> [f a]
- linearProjSubgrad :: (Additive f, Traversable f, Metric f, Ord a, Fractional a) => StepSched f a -> (f a -> f a) -> f a -> a -> f a -> [f a]
- type StepSched f a = [f a -> a -> a]
- optimalStepSched :: (Fractional a, Metric f) => a -> StepSched f a
- constStepSched :: a -> StepSched f a
- sqrtKStepSched :: Floating a => a -> StepSched f a
- invKStepSched :: Fractional a => a -> StepSched f a
- data Constraint f a = Constr Ordering a (f a)
- linearProjection :: (Fractional a, Ord a, RealFloat a, Metric f) => [Constraint f a] -> f a -> f a
Projected subgradient method
Arguments
| :: (Additive f, Traversable f, Metric f, Ord a, Fractional a) | |
| => StepSched f a | A step size schedule |
| -> (f a -> f a) | Function projecting into the feasible space |
| -> (f a -> f a) | Gradient of objective function |
| -> (f a -> a) | The objective function |
| -> f a | Initial solution |
| -> [f a] |
projSubgrad stepSizes proj a b x0 minimizes the objective A
x - b potentially projecting iterates into a feasible space with
proj with the given step-size schedule
Arguments
| :: (Additive f, Traversable f, Metric f, Ord a, Fractional a) | |
| => StepSched f a | A step size schedule |
| -> (f a -> f a) | Function projecting into the feasible space |
| -> f a | Coefficient vector |
| -> a | Constant |
| -> f a | Initial solution |
| -> [f a] |
linearProjSubgrad stepSizes proj a b x0 minimizes the objective A
x - b potentially projecting iterates into a feasible space with
proj with the given step-size schedule
Step schedules
type StepSched f a = [f a -> a -> a]Source
A step size schedule A list of functions (one per step) which, given a function's gradient and value, will provide a size for the next step
Arguments
| :: (Fractional a, Metric f) | |
| => a | The optimal value of the objective |
| -> StepSched f a |
The optimal step size schedule when the optimal value of the objective is known
A non-summable step size schedule
Arguments
| :: Fractional a | |
| => a | The size of the first step |
| -> StepSched f a |
A square-summable step size schedule
Linear constraints
data Constraint f a Source
A linear constraint. For instance, Constr LT 2 (V2 1 3) defines
the constraint x_1 + 3 x_2 <= 2
Instances
| (Show a, Show (f a)) => Show (Constraint f a) |
Arguments
| :: (Fractional a, Ord a, RealFloat a, Metric f) | |
| => [Constraint f a] | A set of linear constraints |
| -> f a | |
| -> f a |
Project onto a the space of feasible solutions defined by a set of linear constraints