Class LBFGSB

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

Limited-memory BFGS for bound-constrained optimization (L-BFGS-B).

public sealed class LBFGSB : OptimizationMethod

Inheritance

object

OptimizationMethod

LBFGSB

Inherited Members

OptimizationMethod.Minimize(Problem, EndCriteria)

OptimizationMethod.Minimize(ProblemState, EndCriteria)

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Faithful implementation of the algorithm of Byrd, Lu, Nocedal and Zhu, "A Limited Memory Algorithm for Bound Constrained Optimization", SIAM J. Sci. Comput. 16(5):1190-1208, 1995.

Coordinates whose bound is ±MaxValue are treated as unbounded, so with no active bounds the method reduces to plain limited-memory BFGS. Explicit bounds may instead be passed to the constructor, overriding the constraint.

Limited memory trades accuracy of the Hessian model for cost: it stores only the last memory correction pairs, needing O(memory·n) storage and work per step instead of the O(n²) of dense BFGS, at the price of linear rather than superlinear convergence. This typically results in a modest increase in iteration count.

Immutable: each minimization keeps its correction pairs and working arrays to itself. On the relative function-reduction stop the problem's gradient norm is the projected gradient's at the point returned, where QuantLib's keeps the previous iterate's (Divergences/LBFGSBTests.cs). The breakpoints of the Cauchy search are sorted stably, so equal breakpoints keep QuantLib's order up to 32 variables (MSVC's insertion sort) and their own beyond, where MSVC's introsort reorders them.

Constructors

LBFGSB(int, double, double)

Initializes a new instance of the LBFGSB class.

public LBFGSB(int memory = 10, double pgTol = 1E-08, double fTol = 2.220446049250313E-09)

Parameters

memory int

The number of stored correction pairs, positive.

pgTol double

The convergence tolerance on the infinity norm of the projected gradient.

fTol double

The iteration stops when the relative reduction of the objective falls below it.

Exceptions

ArgumentOutOfRangeException

memory isn't positive.

LBFGSB(ReadOnlySpan<double>, ReadOnlySpan<double>, int, double, double)

Initializes a new instance of the LBFGSB class with explicit box bounds, which override the bounds of the problem's constraint. Use ±MaxValue for unbounded coordinates.

public LBFGSB(ReadOnlySpan<double> lowerBound, ReadOnlySpan<double> upperBound, int memory = 10, double pgTol = 1E-08, double fTol = 2.220446049250313E-09)

Parameters

lowerBound ReadOnlySpan<double>

The lower bounds, which it copies.

upperBound ReadOnlySpan<double>

The upper bounds, which it copies.

memory int

The number of stored correction pairs, positive.

pgTol double

The convergence tolerance on the infinity norm of the projected gradient.

fTol double

The iteration stops when the relative reduction of the objective falls below it.

Exceptions

ArgumentOutOfRangeException

memory isn't positive.

ArgumentException

The bounds have different sizes.

Methods

MinimizeCore(ProblemState, EndCriteria)

The method's algorithm, QuantLib's minimize: minimizes from the state's current value.

protected override EndCriteriaType MinimizeCore(ProblemState P, EndCriteria endCriteria)

Parameters

P ProblemState

The working state, which the minimization changes.

endCriteria EndCriteria

The criteria that end the minimization.

Returns

EndCriteriaType

The end criterion met.

Exceptions

NanoQLException

The bounds' size doesn't match the number of variables.