Package de.labathome.trustconstr

Class TrustRegionInteriorPoint

java.lang.Object

de.labathome.trustconstr.TrustRegionInteriorPoint

public class TrustRegionInteriorPoint
extends Object

Trust-region interior-point method.

References:

1. Byrd, Hribar, Nocedal, "An interior point algorithm for large-scale nonlinear programming", SIAM J. Optim. 9.4 (1999): 877-900.
2. Byrd, Liu, Nocedal, "On the local behavior of an interior point method for nonlinear programming", Numerical Analysis 1997 (1997): 37-56.
3. Nocedal & Wright, Numerical Optimization, 2nd ed. (2006).

Constructor Summary

Constructors

Constructor	Description
TrustRegionInteriorPoint()

Method Summary

Modifier and Type	Method	Description
static StatefulResult	trustRegionInteriorPoint(ToDoubleBiFunction<Matrix,Object> fun, BiFunction<Matrix,Object,Matrix> grad, LagrangeHessian lagrHess, int nVars, int nIneq, int nEq, Constraint constr, Jacobian jac, Matrix x0, double fun0, Matrix grad0, Matrix constrIneq0, Matrix jacIneq0, Matrix constrEq0, Matrix jacEq0, GlobalStoppingCriteria stopCrit, boolean[] enforceFeasibility, double xtol, State state, double initialBarrierParameter, double initialTolerance, double initialPenalty, double initialTrustRadius, ProjectionMethod factorizationMethod)	Trust-region interior-point solve.

Methods inherited from class java.lang.Object

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

Constructor Details

TrustRegionInteriorPoint

public TrustRegionInteriorPoint()

Method Details

trustRegionInteriorPoint

public static StatefulResult trustRegionInteriorPoint(ToDoubleBiFunction<Matrix,Object> fun,
 BiFunction<Matrix,Object,Matrix> grad,
 LagrangeHessian lagrHess,
 int nVars,
 int nIneq,
 int nEq,
 Constraint constr,
 Jacobian jac,
 Matrix x0,
 double fun0,
 Matrix grad0,
 Matrix constrIneq0,
 Matrix jacIneq0,
 Matrix constrEq0,
 Matrix jacEq0,
 GlobalStoppingCriteria stopCrit,
 boolean[] enforceFeasibility,
 double xtol,
 State state,
 double initialBarrierParameter,
 double initialTolerance,
 double initialPenalty,
 double initialTrustRadius,
 ProjectionMethod factorizationMethod)

Trust-region interior-point solve.

Minimizes

   minimize    fun(x)
   subject to  constr_ineq(x) <= 0
               constr_eq(x)   =  0
 

using the algorithm of Byrd-Hribar-Nocedal (1999).

Parameters:

fun - objective (x, args) -> f(x)

grad - gradient (x, args) -> gradf(x)

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

nVars - number of decision variables

nIneq - number of canonical inequality rows (c(x) <= 0)

nEq - number of canonical equality rows (c(x) = 0)

constr - combined-constraint evaluator that returns (eq, ineq)

jac - combined-constraint Jacobian evaluator

x0 - starting iterate (n x 1)

fun0 - fun(x0)

grad0 - grad(x0)

constrIneq0 - constr_ineq(x0) (nIneq x 1)

jacIneq0 - inequality Jacobian at x0 (nIneq x n)

constrEq0 - constr_eq(x0) (nEq x 1)

jacEq0 - equality Jacobian at x0 (nEq x n)

stopCrit - termination criterion (queried each outer iteration)

enforceFeasibility - per-canonical-ineq flag forcing strict feasibility in the slack rows; may be null (no enforcement)

xtol - termination tolerance on trustRadius

state - mutable iteration state to thread through and return

initialBarrierParameter - initial value of the log-barrier coefficient

initialTolerance - initial inner-loop tolerance for the barrier subproblem

initialPenalty - initial constraint penalty for the merit function

initialTrustRadius - initial trust-region radius

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

Returns:

populated StatefulResult