| Copyright | (c) 2009-2011 Felipe Lessa |
|---|---|
| License | GPL |
| Maintainer | felipe.lessa@gmail.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell98 |
Numeric.Optimization.Algorithms.HagerZhang05
Contents
Description
This module implements the algorithms described by Hager and
Zhang [1]. We use bindings to CG_DESCENT library by the same
authors, version 3.0 from 18/05/2008 [2]. The library code is
also licensed under the terms of the GPL.
- [1] Hager, W. W. and Zhang, H. A new conjugate gradient method with guaranteed descent and an efficient line search. Society of Industrial and Applied Mathematics Journal on Optimization, 16 (2005), 170-192.
- [2] http://www.math.ufl.edu/~hager/papers/CG/CG_DESCENT-C-3.0.tar.gz
- optimize :: Vector v Double => Parameters -> Double -> v Double -> Function t1 -> Gradient t2 -> Maybe (Combined t3) -> IO (Vector Double, Result, Statistics)
- data Function t where
- data Gradient t where
- data Combined t where
- type PointMVector m = MVector (PrimState m) Double
- type GradientMVector m = MVector (PrimState m) Double
- data Simple
- data Mutable
- data Result
- data Statistics = Statistics {
- finalValue :: Double
- gradNorm :: Double
- totalIters :: CInt
- funcEvals :: CInt
- gradEvals :: CInt
- defaultParameters :: Parameters
- data Parameters = Parameters {
- printFinal :: Bool
- printParams :: Bool
- verbose :: Verbose
- lineSearch :: LineSearch
- qdecay :: Double
- stopRules :: StopRules
- estimateError :: EstimateError
- quadraticStep :: Maybe Double
- debugTol :: Maybe Double
- initialStep :: Maybe Double
- maxItersFac :: Double
- nexpand :: CInt
- nsecant :: CInt
- restartFac :: Double
- funcEpsilon :: Double
- nanRho :: Double
- techParameters :: TechParameters
- data Verbose
- = Quiet
- | Verbose
- | VeryVerbose
- data LineSearch
- data StopRules
- data EstimateError
- data TechParameters = TechParameters {}
Main function
Please pay close attention to the types of Vectors and
MVetors being used below. They may come from
Data.Vector.Generic/Data.Vector.Generic.Mutable or from
Data.Vector.Storable/Data.Vector.Storable.Mutable. The
rule of thumb is that input pure vectors are Generic and
everything else is Storable.
Arguments
| :: Vector v Double | |
| => Parameters | How should we optimize. |
| -> Double |
|
| -> v Double | Initial guess. |
| -> Function t1 | Function to be minimized. |
| -> Gradient t2 | Gradient of the function. |
| -> Maybe (Combined t3) | (Optional) Combined function computing both the function and its gradient. |
| -> IO (Vector Double, Result, Statistics) |
Run the CG_DESCENT optimizer and try to minimize the
function.
User-defined function types
Function calculating the value of the objective function f
at a point x.
Function calculating the value of the gradient of the
objective function f at a point x.
The MGradient constructor uses a function receiving as
parameters the point x being evaluated (should not be
modified) and the vector where the gradient should be written.
Function calculating both the value of the objective
function f and its gradient at a point x.
type PointMVector m = MVector (PrimState m) Double Source
Mutable vector representing the point where the function/gradient is begin evaluated. This vector should not be modified.
type GradientMVector m = MVector (PrimState m) Double Source
Mutable vector representing where the gradient should be written.
Kinds of function types
Result and statistics
Constructors
| ToleranceStatisfied | Convergence tolerance was satisfied. |
| FunctionChange | Change in function value was less than |
| MaxTotalIter | Total iterations exceeded |
| NegativeSlope | Slope was always negative in line search. |
| MaxSecantIter | Number of secant iterations exceed nsecant. |
| NotDescent | Search direction not a descent direction. |
| LineSearchFailsInitial | Line search fails in initial interval. |
| LineSearchFailsBisection | Line search fails during bisection. |
| LineSearchFailsUpdate | Line search fails during interval update. |
| DebugTol | Debug tolerance was on and the test failed (see |
| FunctionValueNaN | Function value became |
| StartFunctionValueNaN | Initial function value was |
data Statistics Source
Statistics given after the process finishes.
Constructors
| Statistics | |
Fields
| |
Instances
Options
defaultParameters :: Parameters Source
Default parameters. See the documentation for Parameters
and TechParameters to see what are the defaults.
data Parameters Source
Parameters given to the optimizer.
Constructors
| Parameters | |
Fields
| |
Instances
How verbose we should be.
Constructors
| Quiet | Do not output anything to |
| Verbose | Print what work is being done on each iteraction. |
| VeryVerbose | Print information about every step, may be useful for troubleshooting. |
data LineSearch Source
Line search methods that may be used.
Constructors
| ApproximateWolfe | Use approximate Wolfe line search. |
| AutoSwitch Double | Use ordinary Wolfe line search, switch to approximate Wolfe when |f_{k+1} - f_k| < AWolfeFac * C_kwhere |
Instances
Stop rules used to decided when to stop iterating.
Constructors
| DefaultStopRule Double |
|g_k|_infty <= max(grad_tol, |g_0|_infty * stop_fac) where |
| AlternativeStopRule |
|g_k|_infty <= grad_tol * (1 + |f_k|) |
data EstimateError Source
How to calculate the estimated error in the function value.
Constructors
| AbsoluteEpsilon Double |
|
| RelativeEpsilon Double |
|
Technical parameters
data TechParameters Source
Technical parameters which you probably should not touch.
You should read the papers of CG_DESCENT to understand how
you can tune these parameters.
Constructors
| TechParameters | |
Fields
| |