HMath.Optimization.Local¶

Description

Bounded CPU reference local solvers. Dense quasi-Newton updates implement their named secant formulas; L-BFGS uses a separate two-loop recursion. Scalar Brent combines safeguarded parabolic interpolation and golden steps. Newton-CG uses Hessian products and detects nonpositive curvature.

On this page¶

API	Purpose
ScalarMethod	Bounded one-dimensional minimization strategy (golden section,Brent,or ternary search).
GoldenSection	Declaration and type contract below.
TernarySearch	Declaration and type contract below.
BrentSearch	Declaration and type contract below.
minimizeScalar	Minimize on a finite bracket a<b.
QuasiNewton	Quasi-Newton update selector such as BFGS,DFP,SR1,or limited-memory BFGS.
BFGS	Declaration and type contract below.
LBFGS	Declaration and type contract below.
DFP	Declaration and type contract below.
SR1	Declaration and type contract below.
minimizeQuasiNewton	Run the named inverse-Hessian secant update with safeguarded curvature and a strong-Wolfe descent search.
NewtonMethod	Newton/trust-region strategy selected for checked local minimization.
Newton	Declaration and type contract below.
NewtonCG	Declaration and type contract below.
TrustRegion	Declaration and type contract below.
Dogleg	Declaration and type contract below.
minimizeNewton	Use an analytic square Hessian with Newton/CG or trust-region acceptance; singular systems and collapsed regions fail.
nonlinearCG	Polak–Ribiere+ nonlinear CG with descent restart and strong Wolfe search.
ResidualFunction	Caller-supplied residual vector for nonlinear least-squares fitting.
JacobianFunction	Caller-supplied residual Jacobian with rows corresponding to residual components and columns to parameters.
LeastSquaresLoss	Robust residual penalty selector.
SquaredLoss	Declaration and type contract below.
HuberLoss	Declaration and type contract below.
CauchyLoss	Declaration and type contract below.
SoftL1	Declaration and type contract below.
leastSquares	lambda=0 selects Gauss–Newton, positive lambda selects LM.
nelderMead	Optimize an axis-initialized simplex with reflection, expansion, contraction, and shrink steps; report simplex spread.
powell	Powell direction-set method with bounded line minimization on [-radius,radius].

Documentation

ScalarMethod

data ScalarMethod Source #

Bounded one-dimensional minimization strategy (golden section,Brent,or ternary search).

Constructors

GoldenSection
TernarySearch
BrentSearch

Instances

Instances details

Show ScalarMethod Source #
Instance details Defined in HMath.Optimization.Local Methods showsPrec :: Int -> ScalarMethod -> ShowS # show :: ScalarMethod -> String # showList :: [ScalarMethod] -> ShowS #
Eq ScalarMethod Source #
Instance details Defined in HMath.Optimization.Local Methods (==) :: ScalarMethod -> ScalarMethod -> Bool # (/=) :: ScalarMethod -> ScalarMethod -> Bool #

minimizeScalar

minimizeScalar :: ScalarMethod -> OptimizeOptions -> (Double -> Either MathError Double) -> Double -> Double -> Either MathError OptimizeResult Source #

Minimize on a finite bracket a<b. Result residual is interval width, not an unconstrained derivative.

QuasiNewton

data QuasiNewton Source #

Quasi-Newton update selector such as BFGS,DFP,SR1,or limited-memory BFGS.

Constructors

BFGS
LBFGS Int
DFP
SR1

Instances

Instances details

Show QuasiNewton Source #
Instance details Defined in HMath.Optimization.Local Methods showsPrec :: Int -> QuasiNewton -> ShowS # show :: QuasiNewton -> String # showList :: [QuasiNewton] -> ShowS #
Eq QuasiNewton Source #
Instance details Defined in HMath.Optimization.Local Methods (==) :: QuasiNewton -> QuasiNewton -> Bool # (/=) :: QuasiNewton -> QuasiNewton -> Bool #

minimizeQuasiNewton

minimizeQuasiNewton :: QuasiNewton -> OptimizeOptions -> Objective -> Gradient -> [Double] -> Either MathError OptimizeResult Source #

Run the named inverse-Hessian secant update with safeguarded curvature and a strong-Wolfe descent search.

NewtonMethod

data NewtonMethod Source #

Newton/trust-region strategy selected for checked local minimization.

Constructors

Newton
NewtonCG
TrustRegion Double
Dogleg Double

Instances

Instances details

Show NewtonMethod Source #
Instance details Defined in HMath.Optimization.Local Methods showsPrec :: Int -> NewtonMethod -> ShowS # show :: NewtonMethod -> String # showList :: [NewtonMethod] -> ShowS #
Eq NewtonMethod Source #
Instance details Defined in HMath.Optimization.Local Methods (==) :: NewtonMethod -> NewtonMethod -> Bool # (/=) :: NewtonMethod -> NewtonMethod -> Bool #

minimizeNewton

minimizeNewton :: NewtonMethod -> OptimizeOptions -> Objective -> Gradient -> Hessian -> [Double] -> Either MathError OptimizeResult Source #

Use an analytic square Hessian with Newton/CG or trust-region acceptance; singular systems and collapsed regions fail.

nonlinearCG

nonlinearCG :: OptimizeOptions -> Objective -> Gradient -> [Double] -> Either MathError OptimizeResult Source #

Polak–Ribiere+ nonlinear CG with descent restart and strong Wolfe search.

ResidualFunction

type ResidualFunction = [Double] -> Either MathError [Double] Source #

Caller-supplied residual vector for nonlinear least-squares fitting.

JacobianFunction

type JacobianFunction = [Double] -> Either MathError [[Double]] Source #

Caller-supplied residual Jacobian with rows corresponding to residual components and columns to parameters.

LeastSquaresLoss

data LeastSquaresLoss Source #

Robust residual penalty selector. Parameterized HuberCauchySoftL1 choices carry the selected scale; checked solvers validate it.

Constructors

SquaredLoss
HuberLoss Double
CauchyLoss Double
SoftL1 Double

Instances

Instances details

Show LeastSquaresLoss Source #
Instance details Defined in HMath.Optimization.Local Methods showsPrec :: Int -> LeastSquaresLoss -> ShowS # show :: LeastSquaresLoss -> String # showList :: [LeastSquaresLoss] -> ShowS #
Eq LeastSquaresLoss Source #
Instance details Defined in HMath.Optimization.Local Methods (==) :: LeastSquaresLoss -> LeastSquaresLoss -> Bool # (/=) :: LeastSquaresLoss -> LeastSquaresLoss -> Bool #

leastSquares

leastSquares :: LeastSquaresLoss -> Double -> OptimizeOptions -> ResidualFunction -> JacobianFunction -> [Double] -> Either MathError OptimizeResult Source #

lambda=0 selects Gauss–Newton, positive lambda selects LM. Robust losses use iteratively reweighted least squares with the actual robust objective.

nelderMead

nelderMead :: OptimizeOptions -> Objective -> [Double] -> Either MathError OptimizeResult Source #

Optimize an axis-initialized simplex with reflection, expansion, contraction, and shrink steps; report simplex spread.

powell

powell :: Double -> OptimizeOptions -> Objective -> [Double] -> Either MathError OptimizeResult Source #

Powell direction-set method with bounded line minimization on [-radius,radius]. Each outer iteration replaces the direction with greatest decrease by its net displacement, provided that displacement improves the objective.