Regularisation Constraints

PortfolioOptimisers.set_l1_regularisation! Function

set_l1_regularisation!(args...)

No-op fallback for L1 regularisation setup.

Called when no L1 regularisation is configured. Returns nothing.

Mathematical definition

$$\begin{array}{rl}\text{penalty}& ={\lambda }_1\parallel \mathit{w}{\parallel }_1.\end{array}$$

Where:

• ${\lambda }_1$: L1 regularisation coefficient.

• $\mathit{w}$: Portfolio weights vector $N\times 1$.

Related

• LpRegularisation

• set_lp_regularisation!

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PortfolioOptimisers.set_l2_regularisation! Function

set_l2_regularisation!(args...)

No-op fallback for L2 regularisation setup.

Called when no L2 regularisation is configured. Returns nothing.

Mathematical definition

$$\begin{array}{rl}\text{penalty}& ={\lambda }_2\parallel \mathit{w}{\parallel }_2.\end{array}$$

Where:

• ${\lambda }_2$: L2 regularisation coefficient.

• $\mathit{w}$: Portfolio weights vector $N\times 1$.

Related

• LpRegularisation

• set_lp_regularisation!

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PortfolioOptimisers.set_lp_regularisation! Function

set_lp_regularisation!(args...)

No-op fallback for Lp regularisation setup.

Called when no Lp regularisation is configured. Returns nothing.

Related

• LpRegularisation

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PortfolioOptimisers.set_linf_regularisation! Function

set_linf_regularisation!(args...)

No-op fallback for L∞ regularisation setup.

Called when no L∞ regularisation is configured. Returns nothing.

Mathematical definition

$$\begin{array}{rl}\text{penalty}& ={\lambda }_{\mathrm{\infty }}\parallel \mathit{w}{\parallel }_{\mathrm{\infty }}.\end{array}$$

Where:

• ${\lambda }_{\mathrm{\infty }}$: L∞ regularisation coefficient.

• $\mathit{w}$: Portfolio weights vector $N\times 1$.

Related

• LpRegularisation

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PortfolioOptimisers.AbstractRegularisationEstimator Type

abstract type AbstractRegularisationEstimator <: AbstractEstimator

Abstract supertype for all portfolio weight regularisation estimators.

Related

• LpRegularisation

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PortfolioOptimisers.LpRegularisation Type

struct LpRegularisation{__T_p, __T_val} <: AbstractRegularisationEstimator

Lp-norm regularisation term added to the optimisation objective.

Mathematical definition

$$\begin{array}{rl}\text{penalty}& =\mathrm{val}\cdot {(\sum _{i=1}^N|w_i{|}^p)}^{1/p}.\end{array}$$

Where:

• $\mathrm{val}$: Regularisation coefficient.

• $w_i$: Portfolio weight for asset $i$.

• $p>1$: Norm order.

• $N$: Number of assets.

Penalises concentrated portfolios by encouraging weight smoothness for $p>1$.

Fields

• p: Power or order parameter.

• val: Default value to use for the estimator. If nothing, the estimator provides the default value.

Constructors

LpRegularisation(; p::Number = 3, val::Number = 1e-3) -> LpRegularisation

Keywords correspond to the struct's fields.

Validation

• isfinite(p).

• p > 1.

• val > 0 and finite.

Related

• AbstractRegularisationEstimator

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PortfolioOptimisers.VecLpReg Type

const VecLpReg = AbstractVector{<:LpRegularisation}

Alias for a vector of LpRegularisation objects.

Represents a collection of Lp-norm regularisation terms to be added to the optimisation objective.

Related

• LpRegularisation

• LpReg_VecLpReg

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PortfolioOptimisers.LpReg_VecLpReg Type

const LpReg_VecLpReg = Union{<:LpRegularisation, <:VecLpReg}

Alias for a single or vector of Lp regularisation terms.

Matches either a single LpRegularisation or a vector of them (VecLpReg).

Related

• LpRegularisation

• VecLpReg

• set_lp_regularisation!

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