Package de.labathome.trustconstr

Class EqualityConstrainedSQP

java.lang.Object

de.labathome.trustconstr.EqualityConstrainedSQP

public class EqualityConstrainedSQP
extends Object

Byrd-Omojokun Trust-Region SQP method

Constructor Summary

Constructors

Constructor	Description
EqualityConstrainedSQP()

Method Summary

Modifier and Type	Method	Description
static final LinearOperator	defaultScaling(long n)	Default scaling: returns the n x n identity, i.e. an unscaled SQP step.
static StatefulResult	eqSQP(IFunctionAndConstraint funAndConstr, IGradientAndJacobian gradAndJac, LagrangeHessian lagrHess, Matrix x0, double fun0, Matrix grad0, Matrix constr0, Matrix jac0, StoppingCriterion stopCrit, State state, double initialPenalty, double initialTrustRadius, ProjectionMethod factorizationMethod, Matrix trustLb, Matrix trustUb, LinearOperator scaling)	Solve a nonlinear equality-constrained problem using trust-region SQP.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

EqualityConstrainedSQP

public EqualityConstrainedSQP()

Method Details

defaultScaling

public static final LinearOperator defaultScaling(long n)

Default scaling: returns the n x n identity, i.e. an unscaled SQP step. Mirrors scipy's default_scaling, which returns scipy.sparse.eye(n).

Parameters:

n - number of decision variables

Returns:

a LinearOperator that ignores its input and returns the identity

eqSQP

public static StatefulResult eqSQP(IFunctionAndConstraint funAndConstr,
 IGradientAndJacobian gradAndJac,
 LagrangeHessian lagrHess,
 Matrix x0,
 double fun0,
 Matrix grad0,
 Matrix constr0,
 Matrix jac0,
 StoppingCriterion stopCrit,
 State state,
 double initialPenalty,
 double initialTrustRadius,
 ProjectionMethod factorizationMethod,
 Matrix trustLb,
 Matrix trustUb,
 LinearOperator scaling)

Solve a nonlinear equality-constrained problem using trust-region SQP.

Minimizes

   minimize    fun(x)
   subject to  constr(x) = 0
 

using the Byrd-Omojokun trust-region SQP method (Lalee, Nocedal, Plantenga, 1998). Implementation details follow Byrd-Hribar-Nocedal (1999) and Nocedal & Wright, Numerical Optimization, 2nd ed. (2006), p.549.

Parameters:

funAndConstr - combined evaluator returning (f(x), constr(x))

gradAndJac - combined evaluator returning (gradf(x), gradconstr(x))

lagrHess - Hessian-of-Lagrangian (x, v) -> grad^2L(x, v)

x0 - starting iterate (n x 1)

fun0 - fun(x0)

grad0 - grad(x0)

constr0 - constr(x0) (m x 1)

jac0 - constraint Jacobian at x0 (m x n)

stopCrit - termination predicate, queried each outer iteration

state - mutable iteration state to thread through and return

initialPenalty - initial constraint penalty for the merit function

initialTrustRadius - initial trust-region radius

factorizationMethod - projection-Jacobian factorization method (AUGMENTED_SYSTEM / QR_FACTORIZATION / SVD_FACTORIZATION)

trustLb - element-wise lower bounds on the SQP step

trustUb - element-wise upper bounds on the SQP step

scaling - diagonal-scaling operator for the trust-region step (defaultScaling(long) for the identity)

Returns:

populated StatefulResult