[Solvers]

Table of Contents

• Available objects and their input file syntax
  • Newton
  • NewtonWithLineSearch
  • NewtonWithTrustRegion

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Type name written in PascalCase typically refer to a NEML2 object type, oftentimes a primitive tensor type.

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Available objects and their input file syntax

Refer to System Documentation for detailed explanation about this system.

Newton

The standard Newton-Raphson solver which always takes the 'full' Newton step.

abs_tol Absolute tolerance in the convergence criteria

• Type: number
• Default: 1e-10

max_its Maximum number of iterations allowed before issuing an error/exception

• Type: number
• Default: 100

rel_tol Relative tolerance in the convergence criteria

• Type: number
• Default: 1e-08

verbose Verbosity of the solver

• Type: bool
• Default: false

Detailed documentation link

NewtonWithLineSearch

The Newton-Raphson solver with line search.

abs_tol Absolute tolerance in the convergence criteria

• Type: number
• Default: 1e-10

check_negative_critertia_value Whether to check if the convergence criteria for line search becomes negative

• Type: bool
• Default: false

linesearch_cutback Linesearch cut-back factor when the current scale factor cannot sufficiently reduce the residual.

• Type: number
• Default: 2

linesearch_stopping_criteria The lineseach tolerance slightly relaxing the definition of residual decrease

• Type: number
• Default: 0.001

linesearch_type The type of linesearch used.Default: BACKTRACKING. Options are STRONG_WOLFE, BACKTRACKING

• Type: EnumSelection
• Default: BACKTRACKING

max_its Maximum number of iterations allowed before issuing an error/exception

• Type: number
• Default: 100

max_linesearch_iterations Maximum allowable linesearch iterations. No error is produced upon reaching the maximum number of iterations, and the scale factor in the last iteration is used to scale the step.

• Type: number
• Default: 10

rel_tol Relative tolerance in the convergence criteria

• Type: number
• Default: 1e-08

verbose Verbosity of the solver

• Type: bool
• Default: false

Detailed documentation link

NewtonWithTrustRegion

A trust-region Newton solver. The step size and direction are modified by solving a constrained minimization problem using the local quadratic approximation. The default solver parameters are chosen based on a limited set of problems we tested on and are expected to be tuned.

abs_tol Absolute tolerance in the convergence criteria

• Type: number
• Default: 1e-10

accept_criteria Reject the current step when the merit function reduction is below this threshold

• Type: number
• Default: 0.1

delta_0 Initial trust region radius

• Type: number
• Default: 1

delta_max Maximum trust region radius

• Type: number
• Default: 10

expand_criteria The trust region radius is increased when the merit function reduction is above this threshold

• Type: number
• Default: 0.75

expand_factor Factor to apply when increasing the trust region radius

• Type: number
• Default: 2

max_its Maximum number of iterations allowed before issuing an error/exception

• Type: number
• Default: 100

reduce_criteria The trust region radius is reduced when the merit function reduction is below this threshold

• Type: number
• Default: 0.25

reduce_factor Factor to apply when reducing the trust region radius

• Type: number
• Default: 0.25

rel_tol Relative tolerance in the convergence criteria

• Type: number
• Default: 1e-08

subproblem_abs_tol Absolute tolerance used for the quadratic sub-problem

• Type: number
• Default: 1e-08

subproblem_max_its Maximum number of allowable iterations when solving the quadratic sub-problem

• Type: number
• Default: 10

subproblem_rel_tol Relative tolerance used for the quadratic sub-problem

• Type: number
• Default: 1e-06

verbose Verbosity of the solver

• Type: bool
• Default: false

Detailed documentation link