1 /* 2 Context for a Newton trust-region, line-search method for unconstrained 3 minimization 4 */ 5 6 #if !defined(__TAO_NTL_H) 7 #define __TAO_NTL_H 8 #include <petsc/private/taoimpl.h> 9 10 typedef struct { 11 Mat M; 12 PC bfgs_pre; 13 14 Vec W; 15 Vec Xold; 16 Vec Gold; 17 18 /* Parameters when updating the trust-region radius based on steplength 19 20 if step < nu1 (very bad step) 21 radius = omega1 * min(norm(d), radius) 22 elif step < nu2 (bad step) 23 radius = omega2 * min(norm(d), radius) 24 elif step < nu3 (okay step) 25 radius = omega3 * radius; 26 elif step < nu4 (good step) 27 radius = max(omega4 * norm(d), radius) 28 else (very good step) 29 radius = max(omega5 * norm(d), radius) 30 fi 31 */ 32 33 PetscReal nu1; /* used to compute trust-region radius */ 34 PetscReal nu2; /* used to compute trust-region radius */ 35 PetscReal nu3; /* used to compute trust-region radius */ 36 PetscReal nu4; /* used to compute trust-region radius */ 37 38 PetscReal omega1; /* factor used for trust-region update */ 39 PetscReal omega2; /* factor used for trust-region update */ 40 PetscReal omega3; /* factor used for trust-region update */ 41 PetscReal omega4; /* factor used for trust-region update */ 42 PetscReal omega5; /* factor used for trust-region update */ 43 44 /* Parameters when updating the trust-region radius based on reduction 45 46 kappa = ared / pred 47 if kappa < eta1 (very bad step) 48 radius = alpha1 * min(norm(d), radius) 49 elif kappa < eta2 (bad step) 50 radius = alpha2 * min(norm(d), radius) 51 elif kappa < eta3 (okay step) 52 radius = alpha3 * radius; 53 elif kappa < eta4 (good step) 54 radius = max(alpha4 * norm(d), radius) 55 else (very good step) 56 radius = max(alpha5 * norm(d), radius) 57 fi 58 */ 59 60 PetscReal eta1; /* used to compute trust-region radius */ 61 PetscReal eta2; /* used to compute trust-region radius */ 62 PetscReal eta3; /* used to compute trust-region radius */ 63 PetscReal eta4; /* used to compute trust-region radius */ 64 65 PetscReal alpha1; /* factor used for trust-region update */ 66 PetscReal alpha2; /* factor used for trust-region update */ 67 PetscReal alpha3; /* factor used for trust-region update */ 68 PetscReal alpha4; /* factor used for trust-region update */ 69 PetscReal alpha5; /* factor used for trust-region update */ 70 71 /* Parameters when updating the trust-region radius based on interpolation 72 kappa = ared / pred 73 if kappa >= 1.0 - mu1 (very good step) 74 choose tau in [gamma3, gamma4] 75 radius = max(tau * norm(d), radius) 76 elif kappa >= 1.0 - mu2 (good step) 77 choose tau in [gamma2, gamma3] 78 if (tau >= 1.0) 79 radius = max(tau * norm(d), radius) 80 else 81 radius = tau * min(norm(d), radius) 82 fi 83 else (bad step) 84 choose tau in [gamma1, 1.0] 85 radius = tau * min(norm(d), radius) 86 fi 87 */ 88 89 PetscReal mu1; /* used for model agreement in interpolation */ 90 PetscReal mu2; /* used for model agreement in interpolation */ 91 92 PetscReal gamma1; /* factor used for interpolation */ 93 PetscReal gamma2; /* factor used for interpolation */ 94 PetscReal gamma3; /* factor used for interpolation */ 95 PetscReal gamma4; /* factor used for interpolation */ 96 97 PetscReal theta; /* factor used for interpolation */ 98 99 /* Parameters when initializing trust-region radius based on interpolation */ 100 PetscReal mu1_i; /* used for model agreement in interpolation */ 101 PetscReal mu2_i; /* used for model agreement in interpolation */ 102 103 PetscReal gamma1_i; /* factor used for interpolation */ 104 PetscReal gamma2_i; /* factor used for interpolation */ 105 PetscReal gamma3_i; /* factor used for interpolation */ 106 PetscReal gamma4_i; /* factor used for interpolation */ 107 108 PetscReal theta_i; /* factor used for interpolation */ 109 110 /* Other parameters */ 111 PetscReal min_radius; /* lower bound on initial radius value */ 112 PetscReal max_radius; /* upper bound on trust region radius */ 113 PetscReal epsilon; /* tolerance used when computing ared/pred */ 114 115 PetscInt ntrust; /* Trust-region steps accepted */ 116 PetscInt newt; /* Newton directions attempted */ 117 PetscInt bfgs; /* BFGS directions attempted */ 118 PetscInt grad; /* Gradient directions attempted */ 119 120 PetscInt init_type; /* Trust-region initialization method */ 121 PetscInt update_type; /* Trust-region update method */ 122 } TAO_NTL; 123 124 #endif /* if !defined(__TAO_NTL_H) */ 125