Implemented the Shubert-Piyavskii method for minimization

The Shubert-Piyavskii method optimizes a univariate, Lipschitz continuous function inside a specified interval. Given an accurate Lipschitz constant, it is guaranteed to come within an arbitrary epsilon of the true global minimum. Unlike most other deterministic global optimizations algorithm (e.g., golden-section search), it is not restricted to unimodal functions; moreover, it does not require an initial guess. It deterministically samples points from ever-narrowing subintervals of the search space until the sampled best point is sufficiently close to the lower bound given by the Lipschitz constant.

I have added an implementation of an SP solver in crates/argmin/src/solver/shubertpiyavskii/, modifying crates/argmin/src/lib.rs and crates/argmin/src/solver/mod.rs accordingly. Additionally, I have added an example run of the solver to examples/shubertpiyavskii/.

Author: Luis-Varona

crates/argmin/src/lib.rs

@@ -45,7 +45,7 @@
 //!   - [Cauchy point method](`crate::solver::trustregion::CauchyPoint`)
 //!   - [Dogleg method](`crate::solver::trustregion::Dogleg`)
 //!   - [Steihaug method](`crate::solver::trustregion::Steihaug`)
-//!   
+//!
 //! - [Steepest descent](`crate::solver::gradientdescent::SteepestDescent`)
 //!
 //! - [Conjugate gradient methods](`crate::solver::conjugategradient`)
@@ -69,6 +69,8 @@
 //!
 //! - [Golden-section search](`crate::solver::goldensectionsearch::GoldenSectionSearch`)
 //!
+//! - [Shubert-Piyavskii method](`crate::solver::shubertpiyavskii::ShubertPiyavskii`)
+//!
 //! - [Landweber iteration](`crate::solver::landweber::Landweber`)
 //!
 //! - [Brent's methods](`crate::solver::brent`)

crates/argmin/src/solver/mod.rs

@@ -16,5 +16,6 @@ pub mod neldermead;
 pub mod newton;
 pub mod particleswarm;
 pub mod quasinewton;
+pub mod shubertpiyavskii;
 pub mod simulatedannealing;
 pub mod trustregion;