SpectralProjectedGradient

optimization_solvers::steepest_descent::spg

Struct SpectralProjectedGradient 

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pub struct SpectralProjectedGradient { /* private fields */ }

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impl SpectralProjectedGradient

Auto-generated by derive_getters::Getters.

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pub fn grad_tol(&self) -> &Floating

Get field grad_tol from instance of SpectralProjectedGradient.

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pub fn x(&self) -> &DVector<Floating>

Get field x from instance of SpectralProjectedGradient.

Examples found in repository?
examples/spg_example.rs (line 72)
6fn main() {
7    // Setting up logging
8    std::env::set_var("RUST_LOG", "info");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10
11    // Convex function: f(x,y) = x^2 + y^2 + exp(x^2 + y^2)
12    // This function is convex and has a minimum at (0, 0)
13    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
14        let x1 = x[0];
15        let x2 = x[1];
16
17        // Function value
18        let f = x1.powi(2) + x2.powi(2) + (x1.powi(2) + x2.powi(2)).exp();
19
20        // Gradient
21        let exp_term = (x1.powi(2) + x2.powi(2)).exp();
22        let g1 = 2.0 * x1 * (1.0 + exp_term);
23        let g2 = 2.0 * x2 * (1.0 + exp_term);
24        let g = DVector::from_vec(vec![g1, g2]);
25
26        FuncEvalMultivariate::new(f, g)
27    };
28
29    // Setting up the line search (backtracking)
30    let armijo_factor = 1e-4;
31    let beta = 0.5;
32    let mut ls = BackTracking::new(armijo_factor, beta);
33
34    // Setting up the solver with box constraints
35    let tol = 1e-6;
36    let x0 = DVector::from_vec(vec![0.5, 0.5]); // Starting point
37    let lower_bound = DVector::from_vec(vec![-1.0, -1.0]); // -1 <= x <= 1, -1 <= y <= 1
38    let upper_bound = DVector::from_vec(vec![1.0, 1.0]);
39
40    // Create a mutable oracle for SPG initialization
41    let mut oracle_for_init = f_and_g;
42    let mut solver = SpectralProjectedGradient::new(
43        tol,
44        x0.clone(),
45        &mut oracle_for_init,
46        lower_bound.clone(),
47        upper_bound.clone(),
48    );
49
50    // Running the solver
51    let max_iter_solver = 100;
52    let max_iter_line_search = 20;
53
54    println!("=== Spectral Projected Gradient (SPG) Example ===");
55    println!("Objective: f(x,y) = x^2 + y^2 + exp(x^2 + y^2) (convex)");
56    println!("Global minimum: (0, 0) with f(0,0) = 1");
57    println!("Constraints: -1 <= x <= 1, -1 <= y <= 1");
58    println!("Starting point: {:?}", x0);
59    println!("Lower bounds: {:?}", lower_bound);
60    println!("Upper bounds: {:?}", upper_bound);
61    println!("Tolerance: {}", tol);
62    println!();
63
64    match solver.minimize(
65        &mut ls,
66        f_and_g,
67        max_iter_solver,
68        max_iter_line_search,
69        None,
70    ) {
71        Ok(()) => {
72            let x = solver.x();
73            let eval = f_and_g(x);
74            println!("✅ Optimization completed successfully!");
75            println!("Final iterate: {:?}", x);
76            println!("Function value: {:.6}", eval.f());
77            println!("Gradient norm: {:.6}", eval.g().norm());
78            println!("Iterations: {}", solver.k());
79
80            // Check constraint satisfaction
81            println!("Constraint satisfaction:");
82            for i in 0..x.len() {
83                println!(
84                    "  x[{}] = {:.6} (bounds: [{:.1}, {:.1}])",
85                    i, x[i], lower_bound[i], upper_bound[i]
86                );
87            }
88
89            // Check if we're close to the known minimum
90            let true_min = DVector::from_vec(vec![0.0, 0.0]);
91            let distance_to_min = (x - true_min).norm();
92            println!("Distance to true minimum: {:.6}", distance_to_min);
93            println!("Expected function value: 1.0");
94
95            // Show some properties of SPG
96            println!("SPG properties:");
97            println!("  - Uses spectral step length estimation");
98            println!("  - Handles box constraints efficiently");
99            println!("  - Often faster than standard projected gradient");
100        }
101        Err(e) => {
102            println!("❌ Optimization failed: {:?}", e);
103        }
104    }
105}
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pub fn k(&self) -> &usize

Get field k from instance of SpectralProjectedGradient.

Examples found in repository?
examples/spg_example.rs (line 78)
6fn main() {
7    // Setting up logging
8    std::env::set_var("RUST_LOG", "info");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10
11    // Convex function: f(x,y) = x^2 + y^2 + exp(x^2 + y^2)
12    // This function is convex and has a minimum at (0, 0)
13    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
14        let x1 = x[0];
15        let x2 = x[1];
16
17        // Function value
18        let f = x1.powi(2) + x2.powi(2) + (x1.powi(2) + x2.powi(2)).exp();
19
20        // Gradient
21        let exp_term = (x1.powi(2) + x2.powi(2)).exp();
22        let g1 = 2.0 * x1 * (1.0 + exp_term);
23        let g2 = 2.0 * x2 * (1.0 + exp_term);
24        let g = DVector::from_vec(vec![g1, g2]);
25
26        FuncEvalMultivariate::new(f, g)
27    };
28
29    // Setting up the line search (backtracking)
30    let armijo_factor = 1e-4;
31    let beta = 0.5;
32    let mut ls = BackTracking::new(armijo_factor, beta);
33
34    // Setting up the solver with box constraints
35    let tol = 1e-6;
36    let x0 = DVector::from_vec(vec![0.5, 0.5]); // Starting point
37    let lower_bound = DVector::from_vec(vec![-1.0, -1.0]); // -1 <= x <= 1, -1 <= y <= 1
38    let upper_bound = DVector::from_vec(vec![1.0, 1.0]);
39
40    // Create a mutable oracle for SPG initialization
41    let mut oracle_for_init = f_and_g;
42    let mut solver = SpectralProjectedGradient::new(
43        tol,
44        x0.clone(),
45        &mut oracle_for_init,
46        lower_bound.clone(),
47        upper_bound.clone(),
48    );
49
50    // Running the solver
51    let max_iter_solver = 100;
52    let max_iter_line_search = 20;
53
54    println!("=== Spectral Projected Gradient (SPG) Example ===");
55    println!("Objective: f(x,y) = x^2 + y^2 + exp(x^2 + y^2) (convex)");
56    println!("Global minimum: (0, 0) with f(0,0) = 1");
57    println!("Constraints: -1 <= x <= 1, -1 <= y <= 1");
58    println!("Starting point: {:?}", x0);
59    println!("Lower bounds: {:?}", lower_bound);
60    println!("Upper bounds: {:?}", upper_bound);
61    println!("Tolerance: {}", tol);
62    println!();
63
64    match solver.minimize(
65        &mut ls,
66        f_and_g,
67        max_iter_solver,
68        max_iter_line_search,
69        None,
70    ) {
71        Ok(()) => {
72            let x = solver.x();
73            let eval = f_and_g(x);
74            println!("✅ Optimization completed successfully!");
75            println!("Final iterate: {:?}", x);
76            println!("Function value: {:.6}", eval.f());
77            println!("Gradient norm: {:.6}", eval.g().norm());
78            println!("Iterations: {}", solver.k());
79
80            // Check constraint satisfaction
81            println!("Constraint satisfaction:");
82            for i in 0..x.len() {
83                println!(
84                    "  x[{}] = {:.6} (bounds: [{:.1}, {:.1}])",
85                    i, x[i], lower_bound[i], upper_bound[i]
86                );
87            }
88
89            // Check if we're close to the known minimum
90            let true_min = DVector::from_vec(vec![0.0, 0.0]);
91            let distance_to_min = (x - true_min).norm();
92            println!("Distance to true minimum: {:.6}", distance_to_min);
93            println!("Expected function value: 1.0");
94
95            // Show some properties of SPG
96            println!("SPG properties:");
97            println!("  - Uses spectral step length estimation");
98            println!("  - Handles box constraints efficiently");
99            println!("  - Often faster than standard projected gradient");
100        }
101        Err(e) => {
102            println!("❌ Optimization failed: {:?}", e);
103        }
104    }
105}
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pub fn lower_bound(&self) -> &DVector<Floating>

Get field lower_bound from instance of SpectralProjectedGradient.

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pub fn upper_bound(&self) -> &DVector<Floating>

Get field upper_bound from instance of SpectralProjectedGradient.

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pub fn lambda(&self) -> &Floating

Get field lambda from instance of SpectralProjectedGradient.

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pub fn lambda_min(&self) -> &Floating

Get field lambda_min from instance of SpectralProjectedGradient.

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pub fn lambda_max(&self) -> &Floating

Get field lambda_max from instance of SpectralProjectedGradient.

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impl SpectralProjectedGradient

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pub fn with_lambdas(self, lambda_min: Floating, lambda_max: Floating) -> Self

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pub fn new( grad_tol: Floating, x0: DVector<Floating>, oracle: &mut impl FnMut(&DVector<Floating>) -> FuncEvalMultivariate, lower_bound: DVector<Floating>, upper_bound: DVector<Floating>, ) -> Self

Examples found in repository?
examples/spg_example.rs (lines 42-48)
6fn main() {
7    // Setting up logging
8    std::env::set_var("RUST_LOG", "info");
9    let _ = Tracer::default().with_normal_stdout_layer().build();
10
11    // Convex function: f(x,y) = x^2 + y^2 + exp(x^2 + y^2)
12    // This function is convex and has a minimum at (0, 0)
13    let f_and_g = |x: &DVector<f64>| -> FuncEvalMultivariate {
14        let x1 = x[0];
15        let x2 = x[1];
16
17        // Function value
18        let f = x1.powi(2) + x2.powi(2) + (x1.powi(2) + x2.powi(2)).exp();
19
20        // Gradient
21        let exp_term = (x1.powi(2) + x2.powi(2)).exp();
22        let g1 = 2.0 * x1 * (1.0 + exp_term);
23        let g2 = 2.0 * x2 * (1.0 + exp_term);
24        let g = DVector::from_vec(vec![g1, g2]);
25
26        FuncEvalMultivariate::new(f, g)
27    };
28
29    // Setting up the line search (backtracking)
30    let armijo_factor = 1e-4;
31    let beta = 0.5;
32    let mut ls = BackTracking::new(armijo_factor, beta);
33
34    // Setting up the solver with box constraints
35    let tol = 1e-6;
36    let x0 = DVector::from_vec(vec![0.5, 0.5]); // Starting point
37    let lower_bound = DVector::from_vec(vec![-1.0, -1.0]); // -1 <= x <= 1, -1 <= y <= 1
38    let upper_bound = DVector::from_vec(vec![1.0, 1.0]);
39
40    // Create a mutable oracle for SPG initialization
41    let mut oracle_for_init = f_and_g;
42    let mut solver = SpectralProjectedGradient::new(
43        tol,
44        x0.clone(),
45        &mut oracle_for_init,
46        lower_bound.clone(),
47        upper_bound.clone(),
48    );
49
50    // Running the solver
51    let max_iter_solver = 100;
52    let max_iter_line_search = 20;
53
54    println!("=== Spectral Projected Gradient (SPG) Example ===");
55    println!("Objective: f(x,y) = x^2 + y^2 + exp(x^2 + y^2) (convex)");
56    println!("Global minimum: (0, 0) with f(0,0) = 1");
57    println!("Constraints: -1 <= x <= 1, -1 <= y <= 1");
58    println!("Starting point: {:?}", x0);
59    println!("Lower bounds: {:?}", lower_bound);
60    println!("Upper bounds: {:?}", upper_bound);
61    println!("Tolerance: {}", tol);
62    println!();
63
64    match solver.minimize(
65        &mut ls,
66        f_and_g,
67        max_iter_solver,
68        max_iter_line_search,
69        None,
70    ) {
71        Ok(()) => {
72            let x = solver.x();
73            let eval = f_and_g(x);
74            println!("✅ Optimization completed successfully!");
75            println!("Final iterate: {:?}", x);
76            println!("Function value: {:.6}", eval.f());
77            println!("Gradient norm: {:.6}", eval.g().norm());
78            println!("Iterations: {}", solver.k());
79
80            // Check constraint satisfaction
81            println!("Constraint satisfaction:");
82            for i in 0..x.len() {
83                println!(
84                    "  x[{}] = {:.6} (bounds: [{:.1}, {:.1}])",
85                    i, x[i], lower_bound[i], upper_bound[i]
86                );
87            }
88
89            // Check if we're close to the known minimum
90            let true_min = DVector::from_vec(vec![0.0, 0.0]);
91            let distance_to_min = (x - true_min).norm();
92            println!("Distance to true minimum: {:.6}", distance_to_min);
93            println!("Expected function value: 1.0");
94
95            // Show some properties of SPG
96            println!("SPG properties:");
97            println!("  - Uses spectral step length estimation");
98            println!("  - Handles box constraints efficiently");
99            println!("  - Often faster than standard projected gradient");
100        }
101        Err(e) => {
102            println!("❌ Optimization failed: {:?}", e);
103        }
104    }
105}

Trait Implementations§

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impl ComputeDirection for SpectralProjectedGradient

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fn compute_direction( &mut self, eval: &FuncEvalMultivariate, ) -> Result<DVector<Floating>, SolverError>

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impl HasBounds for SpectralProjectedGradient

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fn lower_bound(&self) -> &DVector<Floating>

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fn set_lower_bound(&mut self, lower_bound: DVector<Floating>)

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fn set_upper_bound(&mut self, upper_bound: DVector<Floating>)

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fn upper_bound(&self) -> &DVector<Floating>

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impl LineSearchSolver for SpectralProjectedGradient

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fn has_converged(&self, eval: &FuncEvalMultivariate) -> bool

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fn xk(&self) -> &DVector<Floating>

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fn xk_mut(&mut self) -> &mut DVector<Floating>

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fn k(&self) -> &usize

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fn k_mut(&mut self) -> &mut usize

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fn update_next_iterate<LS: LineSearch>( &mut self, line_search: &mut LS, eval_x_k: &FuncEvalMultivariate, oracle: &mut impl FnMut(&DVector<Floating>) -> FuncEvalMultivariate, direction: &DVector<Floating>, max_iter_line_search: usize, ) -> Result<(), SolverError>

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fn setup(&mut self)

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fn evaluate_x_k( &mut self, oracle: &mut impl FnMut(&DVector<Floating>) -> FuncEvalMultivariate, ) -> Result<FuncEvalMultivariate, SolverError>

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fn minimize<LS: LineSearch>( &mut self, line_search: &mut LS, oracle: impl FnMut(&DVector<Floating>) -> FuncEvalMultivariate, max_iter_solver: usize, max_iter_line_search: usize, callback: Option<&mut dyn FnMut(&Self)>, ) -> Result<(), SolverError>

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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T> HasProjectedGradient for T
where T: LineSearchSolver + HasBounds,

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fn projected_gradient(&self, eval: &FuncEvalMultivariate) -> DVector<Floating>

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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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