Package parsimony :: Package functions :: Module properties :: Class StronglyConvex

Class StronglyConvex

object --+
         |
        StronglyConvex

Known Subclasses:

Represents strongly convex functions.

A function is strongly convex with parameter m if

    (grad(f(x) - grad(f(y))'(x - y) >= m.||x - y||²_2,

or equivalently if

    H(f(x)) >= mI,

where H is the Hessian, I is the identity matrix. The second ">=" means
that H(f(x)) - mI is positive semi-definite.

Nested Classes

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__metaclass__
Metaclass for defining Abstract Base Classes (ABCs).

Instance Methods

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parameter(self)
Returns the strongly convex parameter for the function.

source code

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __init__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Class Variables

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__abstractmethods__ = frozenset(['parameter'])

_abc_cache = <_weakrefset.WeakSet object at 0x30de050>

_abc_negative_cache = <_weakrefset.WeakSet object at 0x30de0d0>

_abc_negative_cache_version = 10

_abc_registry = <_weakrefset.WeakSet object at 0x30d8f50>

Properties

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Inherited from object: __class__

Method Details

[hide private]

parameter(self)

source code

Returns the strongly convex parameter for the function.

Decorators:

@abc.abstractmethod