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//! Bilevel optimization
//!
//! Provides bilevel programming methods where one optimization problem (the upper level)
//! is nested inside another (the lower level).
//!
//! # Mathematical Formulation
//!
//! ```text
//! min_{x,y} F(x, y) (upper level objective)
//! s.t. G_i(x, y) <= 0 (upper level constraints)
//! y solves:
//! min_y f(x, y) (lower level objective)
//! s.t. g_j(x,y) <= 0 (lower level constraints)
//! ```
//!
//! # Methods
//!
//! - [`SingleLevelReduction`]: KKT-based single-level reformulation
//! - [`solve_bilevel_psoa`]: Penalty-based sequential optimization approach
//! - [`ReplacementAlgorithm`]: Replace lower level with optimal reaction mapping
//!
//! # Example
//!
//! ```no_run
//! use scirs2_optimize::bilevel::{
//! BilevelProblem, BilevelSolverOptions, solve_bilevel_psoa, PsoaOptions,
//! };
//!
//! // Upper level: min_{x,y} (x - 1)^2 + (y - 1)^2
//! // Lower level: min_y (y - x)^2
//! let upper_obj = |x: &[f64], y: &[f64]| -> f64 {
//! (x[0] - 1.0).powi(2) + (y[0] - 1.0).powi(2)
//! };
//! let lower_obj = |x: &[f64], y: &[f64]| -> f64 {
//! (y[0] - x[0]).powi(2)
//! };
//!
//! let problem = BilevelProblem::new(
//! upper_obj,
//! lower_obj,
//! vec![0.0], // x0
//! vec![0.0], // y0
//! );
//!
//! let options = PsoaOptions::default();
//! let result = solve_bilevel_psoa(problem, options).expect("valid input");
//! println!("Upper x: {:?}, Lower y: {:?}", result.x_upper, result.y_lower);
//! ```
pub use ;