SparseNonlinearProgramDerivatives Class

public sealed class SparseNonlinearProgramDerivatives

Public NotInheritable Class SparseNonlinearProgramDerivatives

public ref class SparseNonlinearProgramDerivatives sealed

[<SealedAttribute>]
type SparseNonlinearProgramDerivatives = class end

Inheritance

Object  →  SparseNonlinearProgramDerivatives

The Jacobian contains first derivatives of the constraints, with rows in the original Constraints order and columns in variable order. Pattern callbacks must include every entry that can become nonzero during a solve, including entries currently zero. Value callbacks emit finite entries; repeated entries are added. Omitted entries are zero.

Hessian callbacks emit the lower triangle of weight*f(x)-sum(lambda[i]*c[i](x)). The objective weight is 1 for minimization and -1 for maximization. Multipliers use original constraint order; positive multipliers belong to lower bounds, negative multipliers to upper bounds. Variable bounds have zero curvature. Emit each symmetric entry once. Do not modify or retain input buffers or the supplied entry writer.

Callbacks must be defined at trial points, including points outside variable bounds for the sparse infeasible-start method. For bounds-only Newton-CG, explicitly supplied Gauss-Newton curvature may approximate the objective Hessian; retain the objective weight and original sign conventions. The objective and first derivatives must still describe the original function. Omitting Hessian values permits numerical recovery from the pattern; omitting both Hessian callbacks permits limited-memory BFGS. This type does not change constraint value functions.

Reference