Struct ConvexSubdifferential 

pub struct ConvexSubdifferential {
    pub name: String,
    pub is_differentiable: bool,
    pub strong_convexity_modulus: f64,
    pub is_lipschitz: bool,
    pub lipschitz_constant: f64,
}

Represents a convex function via its subdifferential properties.

Fields

name: String

Name/description of the function.

is_differentiable: bool

Whether the function is differentiable.

strong_convexity_modulus: f64

Whether the function is strongly convex with modulus μ > 0.

is_lipschitz: bool

Whether the function is Lipschitz continuous.

lipschitz_constant: f64

Lipschitz constant L (if is_lipschitz).

Implementations

impl ConvexSubdifferential

pub fn new(name: &str) -> Self

Create a new subdifferential descriptor.

pub fn with_differentiability(self) -> Self

Set differentiability.

pub fn with_strong_convexity(self, mu: f64) -> Self

Set strong convexity modulus μ.

pub fn with_lipschitz(self, l: f64) -> Self

Set Lipschitz constant.

pub fn sum_rule_holds(&self, other: &ConvexSubdifferential) -> bool

Subdifferential sum rule: ∂(f + g)(x) ⊇ ∂f(x) + ∂g(x). Equality holds when regularity condition is satisfied.

pub fn chain_rule_holds(&self) -> bool

Chain rule: ∂(f ∘ A)(x) = A^T ∂f(Ax) under constraint qualification.

pub fn gradient_descent_rate(&self) -> Option<f64>

Fenchel conjugate: optimal convergence rate for gradient descent. With μ-strong convexity and L-smoothness: rate = 1 - μ/L.

pub fn proximal_convergence_rate(&self, k: usize) -> f64

Proximal point algorithm convergence: 1/k rate for convex, linear for strongly convex.