/* Context for bounded Newton-Krylov type optimization algorithms */ #if !defined(__TAO_BNK_H) #define __TAO_BNK_H #include #include <../src/tao/bound/impls/bncg/bncg.h> typedef struct { /* Function pointer for hessian evaluation NOTE: This is necessary so that quasi-Newton-Krylov methods can "evaluate" a quasi-Newton approximation while full Newton-Krylov methods call-back to the application's Hessian */ PetscErrorCode (*computehessian)(Tao); PetscErrorCode (*computestep)(Tao, PetscBool, KSPConvergedReason*, PetscInt*); /* Embedded TAOBNCG */ Tao bncg; TAO_BNCG *bncg_ctx; PetscInt max_cg_its, tot_cg_its; Vec bncg_sol; /* Allocated vectors */ Vec W, Xwork, Gwork, Xold, Gold; Vec unprojected_gradient, unprojected_gradient_old; /* Unallocated matrices and vectors */ Mat H_inactive, Hpre_inactive; Vec X_inactive, G_inactive, inactive_work, active_work; IS inactive_idx, active_idx, active_lower, active_upper, active_fixed; /* Scalar values for the solution and step */ PetscReal fold, f, gnorm, dnorm; /* Parameters for active set estimation */ PetscReal as_tol; PetscReal as_step; /* BFGS preconditioner data */ PC bfgs_pre; Mat M; Vec Diag_min, Diag_max; /* Parameters when updating the perturbation added to the Hessian matrix according to the following scheme: pert = sval; do until convergence shift Hessian by pert solve Newton system if (linear solver failed or did not compute a descent direction) use steepest descent direction and increase perturbation if (0 == pert) initialize perturbation pert = min(imax, max(imin, imfac * norm(G))) else increase perturbation pert = min(pmax, max(pgfac * pert, pmgfac * norm(G))) fi else use linear solver direction and decrease perturbation pert = min(psfac * pert, pmsfac * norm(G)) if (pert < pmin) pert = 0 fi fi perform line search function and gradient evaluation check convergence od */ PetscReal sval; /* Starting perturbation value, default zero */ PetscReal imin; /* Minimum perturbation added during initialization */ PetscReal imax; /* Maximum perturbation added during initialization */ PetscReal imfac; /* Merit function factor during initialization */ PetscReal pert; /* Current perturbation value */ PetscReal pmin; /* Minimim perturbation value */ PetscReal pmax; /* Maximum perturbation value */ PetscReal pgfac; /* Perturbation growth factor */ PetscReal psfac; /* Perturbation shrink factor */ PetscReal pmgfac; /* Merit function growth factor */ PetscReal pmsfac; /* Merit function shrink factor */ /* Parameters when updating the trust-region radius based on steplength if step < nu1 (very bad step) radius = omega1 * min(norm(d), radius) elif step < nu2 (bad step) radius = omega2 * min(norm(d), radius) elif step < nu3 (okay step) radius = omega3 * radius; elif step < nu4 (good step) radius = max(omega4 * norm(d), radius) else (very good step) radius = max(omega5 * norm(d), radius) fi */ PetscReal nu1; /* used to compute trust-region radius */ PetscReal nu2; /* used to compute trust-region radius */ PetscReal nu3; /* used to compute trust-region radius */ PetscReal nu4; /* used to compute trust-region radius */ PetscReal omega1; /* factor used for trust-region update */ PetscReal omega2; /* factor used for trust-region update */ PetscReal omega3; /* factor used for trust-region update */ PetscReal omega4; /* factor used for trust-region update */ PetscReal omega5; /* factor used for trust-region update */ /* Parameters when updating the trust-region radius based on reduction kappa = ared / pred if kappa < eta1 (very bad step) radius = alpha1 * min(norm(d), radius) elif kappa < eta2 (bad step) radius = alpha2 * min(norm(d), radius) elif kappa < eta3 (okay step) radius = alpha3 * radius; elif kappa < eta4 (good step) radius = max(alpha4 * norm(d), radius) else (very good step) radius = max(alpha5 * norm(d), radius) fi */ PetscReal eta1; /* used to compute trust-region radius */ PetscReal eta2; /* used to compute trust-region radius */ PetscReal eta3; /* used to compute trust-region radius */ PetscReal eta4; /* used to compute trust-region radius */ PetscReal alpha1; /* factor used for trust-region update */ PetscReal alpha2; /* factor used for trust-region update */ PetscReal alpha3; /* factor used for trust-region update */ PetscReal alpha4; /* factor used for trust-region update */ PetscReal alpha5; /* factor used for trust-region update */ /* Parameters when updating the trust-region radius based on interpolation kappa = ared / pred if kappa >= 1.0 - mu1 (very good step) choose tau in [gamma3, gamma4] radius = max(tau * norm(d), radius) elif kappa >= 1.0 - mu2 (good step) choose tau in [gamma2, gamma3] if (tau >= 1.0) radius = max(tau * norm(d), radius) else radius = tau * min(norm(d), radius) fi else (bad step) choose tau in [gamma1, 1.0] radius = tau * min(norm(d), radius) fi */ PetscReal mu1; /* used for model agreement in interpolation */ PetscReal mu2; /* used for model agreement in interpolation */ PetscReal gamma1; /* factor used for interpolation */ PetscReal gamma2; /* factor used for interpolation */ PetscReal gamma3; /* factor used for interpolation */ PetscReal gamma4; /* factor used for interpolation */ PetscReal theta; /* factor used for interpolation */ /* Parameters when initializing trust-region radius based on interpolation */ PetscReal mu1_i; /* used for model agreement in interpolation */ PetscReal mu2_i; /* used for model agreement in interpolation */ PetscReal gamma1_i; /* factor used for interpolation */ PetscReal gamma2_i; /* factor used for interpolation */ PetscReal gamma3_i; /* factor used for interpolation */ PetscReal gamma4_i; /* factor used for interpolation */ PetscReal theta_i; /* factor used for interpolation */ /* Other parameters */ PetscReal min_radius; /* lower bound on initial radius value */ PetscReal max_radius; /* upper bound on trust region radius */ PetscReal epsilon; /* tolerance used when computing ared/pred */ PetscReal dmin, dmax; /* upper and lower bounds for the Hessian diagonal vector */ PetscInt newt; /* Newton directions attempted */ PetscInt bfgs; /* BFGS directions attempted */ PetscInt sgrad; /* Scaled gradient directions attempted */ PetscInt grad; /* Gradient directions attempted */ PetscInt as_type; /* Active set estimation method */ PetscInt bfgs_scale_type; /* Scaling matrix to used for the bfgs preconditioner */ PetscInt init_type; /* Trust-region initialization method */ PetscInt update_type; /* Trust-region update method */ /* Trackers for KSP solution type and convergence reasons */ PetscInt ksp_atol; PetscInt ksp_rtol; PetscInt ksp_ctol; PetscInt ksp_negc; PetscInt ksp_dtol; PetscInt ksp_iter; PetscInt ksp_othr; PetscBool is_nash, is_stcg, is_gltr; /* Implementation specific context */ void* ctx; } TAO_BNK; #define BNK_NEWTON 0 #define BNK_BFGS 1 #define BNK_SCALED_GRADIENT 2 #define BNK_GRADIENT 3 #define BNK_INIT_CONSTANT 0 #define BNK_INIT_DIRECTION 1 #define BNK_INIT_INTERPOLATION 2 #define BNK_INIT_TYPES 3 #define BNK_UPDATE_STEP 0 #define BNK_UPDATE_REDUCTION 1 #define BNK_UPDATE_INTERPOLATION 2 #define BNK_UPDATE_TYPES 3 #define BNK_AS_NONE 0 #define BNK_AS_BERTSEKAS 1 #define BNK_AS_TYPES 2 PETSC_INTERN PetscErrorCode TaoCreate_BNK(Tao); PETSC_INTERN PetscErrorCode TaoSetUp_BNK(Tao); PETSC_INTERN PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems*, Tao); PETSC_INTERN PetscErrorCode TaoDestroy_BNK(Tao); PETSC_INTERN PetscErrorCode TaoView_BNK(Tao, PetscViewer); PETSC_INTERN PetscErrorCode TaoSolve_BNLS(Tao); PETSC_INTERN PetscErrorCode TaoSolve_BNTR(Tao); PETSC_INTERN PetscErrorCode TaoSolve_BNTL(Tao); PETSC_INTERN PetscErrorCode TaoBNKPreconBFGS(PC, Vec, Vec); PETSC_INTERN PetscErrorCode TaoBNKInitialize(Tao, PetscInt, PetscBool*); PETSC_INTERN PetscErrorCode TaoBNKEstimateActiveSet(Tao, PetscInt); PETSC_INTERN PetscErrorCode TaoBNKComputeHessian(Tao); PETSC_INTERN PetscErrorCode TaoBNKBoundStep(Tao, PetscInt, Vec); PETSC_INTERN PetscErrorCode TaoBNKTakeCGSteps(Tao, PetscBool*); PETSC_INTERN PetscErrorCode TaoBNKComputeStep(Tao, PetscBool, KSPConvergedReason*, PetscInt*); PETSC_INTERN PetscErrorCode TaoBNKRecomputePred(Tao, Vec, PetscReal*); PETSC_INTERN PetscErrorCode TaoBNKSafeguardStep(Tao, KSPConvergedReason, PetscInt*); PETSC_INTERN PetscErrorCode TaoBNKPerformLineSearch(Tao, PetscInt*, PetscReal*, TaoLineSearchConvergedReason*); PETSC_INTERN PetscErrorCode TaoBNKUpdateTrustRadius(Tao, PetscReal, PetscReal, PetscInt, PetscInt, PetscBool*); PETSC_INTERN PetscErrorCode TaoBNKAddStepCounts(Tao, PetscInt); #endif /* if !defined(__TAO_BNK_H) */