occ::mults::TrustRegion Class Reference

Trust Region Newton optimizer with Steihaug-CG subproblem solver. More...

#include <trust_region.h>

Public Types
using	Objective = std::function< std::pair< double, Vec >(const Vec &)>
	Objective function: returns (value, gradient)
using	HessianFunc = std::function< Mat(const Vec &)>
	Hessian function: returns Hessian matrix.
using	HessianVectorProduct = std::function< Vec(const Vec &, const Vec &)>
	Hessian-vector product: returns H*v (more efficient for large problems)
using	Callback = std::function< bool(int, const Vec &, double, const Vec &)>
	Iteration callback: (iteration, x, value, gradient) -> continue?
using	GradObjective = std::function< double(const Vec &, Vec &)>
	Gradient-only objective: f(x, grad) -> energy (same signature as LBFGS/MSTMIN)

Public Member Functions
	TrustRegion (const TrustRegionSettings &settings={})
TrustRegionResult	minimize (Objective objective, HessianFunc hessian, const Vec &x0, Callback callback=nullptr)
	Minimize using explicit Hessian matrix.
TrustRegionResult	minimize_hvp (Objective objective, HessianVectorProduct hvp, const Vec &x0)
	Minimize using Hessian-vector products (matrix-free).
TrustRegionResult	minimize_bfgs (GradObjective f, const Vec &x0, Callback callback=nullptr)
	Minimize using BFGS Hessian approximation (gradient-only).

Detailed Description

Trust Region Newton optimizer with Steihaug-CG subproblem solver.

This is a robust second-order optimization method that:

• Naturally handles indefinite Hessians (negative curvature)
• Uses analytical Hessians when available
• Solves the trust region subproblem using Steihaug's truncated CG

The trust region subproblem is: min_p g^T p + 0.5 p^T H p subject to ||p|| <= delta

Usage:

TrustRegion optimizer(settings);
auto result = optimizer.minimize(objective, hessian, x0);

Member Typedef Documentation

Callback

using occ::mults::TrustRegion::Callback = std::function<bool(int, const Vec&, double, const Vec&)>

Iteration callback: (iteration, x, value, gradient) -> continue?

GradObjective

using occ::mults::TrustRegion::GradObjective = std::function<double(const Vec&, Vec&)>

Gradient-only objective: f(x, grad) -> energy (same signature as LBFGS/MSTMIN)

HessianFunc

using occ::mults::TrustRegion::HessianFunc = std::function<Mat(const Vec&)>

Hessian function: returns Hessian matrix.

HessianVectorProduct

using occ::mults::TrustRegion::HessianVectorProduct = std::function<Vec(const Vec&, const Vec&)>

Hessian-vector product: returns H*v (more efficient for large problems)

Objective

using occ::mults::TrustRegion::Objective = std::function<std::pair<double, Vec>(const Vec&)>

Objective function: returns (value, gradient)

Constructor & Destructor Documentation

TrustRegion()

occ::mults::TrustRegion::TrustRegion ( const TrustRegionSettings &  settings = {} )

explicit

Member Function Documentation

minimize()

TrustRegionResult occ::mults::TrustRegion::minimize	(	Objective	objective,
		HessianFunc	hessian,
		const Vec &	x0,
		Callback	callback = nullptr
	)

Minimize using explicit Hessian matrix.

Parameters

objective	Function returning (value, gradient)
hessian	Function returning Hessian matrix
x0	Initial parameters
callback	Optional iteration callback (return false to stop)

Returns

Optimization result

minimize_bfgs()

TrustRegionResult occ::mults::TrustRegion::minimize_bfgs	(	GradObjective	f,
		const Vec &	x0,
		Callback	callback = nullptr
	)

Minimize using BFGS Hessian approximation (gradient-only).

Starts from identity Hessian, applies BFGS rank-2 updates each accepted step. No analytic Hessian needed — same interface as LBFGS.

Parameters

f	Gradient-only objective: f(x, grad) -> energy
x0	Initial parameters
callback	Optional iteration callback

Returns

Optimization result

minimize_hvp()

TrustRegionResult occ::mults::TrustRegion::minimize_hvp	(	Objective	objective,
		HessianVectorProduct	hvp,
		const Vec &	x0
	)

Minimize using Hessian-vector products (matrix-free).

Parameters

objective	Function returning (value, gradient)
hvp	Function returning H*v given x and v
x0	Initial parameters

Returns

Optimization result

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The documentation for this class was generated from the following file:

• /home/runner/work/occ/occ/include/occ/mults/trust_region.h