1 #include <../src/tao/bound/impls/bnk/bnk.h> 2 #include <petscksp.h> 3 4 /* 5 Implements Newton's Method with a trust region approach for solving 6 bound constrained minimization problems. 7 8 ------------------------------------------------------------ 9 10 initialize trust radius (default: BNK_INIT_INTERPOLATION) 11 x_0 = VecMedian(x_0) 12 f_0, g_0 = TaoComputeObjectiveAndGradient(x_0) 13 pg_0 = VecBoundGradientProjection(g_0) 14 check convergence at pg_0 15 niter = 0 16 step_accepted = true 17 18 while niter <= max_it 19 if step_accepted 20 niter += 1 21 H_k = TaoComputeHessian(x_k) 22 if pc_type == BNK_PC_BFGS 23 add correction to BFGS approx 24 if scale_type == BNK_SCALE_AHESS 25 D = VecMedian(1e-6, abs(diag(H_k)), 1e6) 26 scale BFGS with VecReciprocal(D) 27 end 28 end 29 end 30 31 if pc_type = BNK_PC_BFGS 32 B_k = BFGS 33 else 34 B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6) 35 B_k = VecReciprocal(B_k) 36 end 37 w = x_k - VecMedian(x_k - 0.001*B_k*g_k) 38 eps = min(eps, norm2(w)) 39 determine the active and inactive index sets such that 40 L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0} 41 U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0} 42 F = {i : l_i = (x_k)_i = u_i} 43 A = {L + U + F} 44 I = {i : i not in A} 45 46 generate the reduced system Hr_k dr_k = -gr_k for variables in I 47 if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS 48 D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6) 49 scale BFGS with VecReciprocal(D) 50 end 51 solve Hr_k dr_k = -gr_k 52 set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F 53 54 x_{k+1} = VecMedian(x_k + d_k) 55 s = x_{k+1} - x_k 56 prered = dot(s, 0.5*gr_k - Hr_k*s) 57 f_{k+1} = TaoComputeObjective(x_{k+1}) 58 actred = f_k - f_{k+1} 59 60 oldTrust = trust 61 step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION) 62 if step_accepted 63 g_{k+1} = TaoComputeGradient(x_{k+1}) 64 pg_{k+1} = VecBoundGradientProjection(g_{k+1}) 65 count the accepted Newton step 66 else 67 f_{k+1} = f_k 68 x_{k+1} = x_k 69 g_{k+1} = g_k 70 pg_{k+1} = pg_k 71 if trust == oldTrust 72 terminate because we cannot shrink the radius any further 73 end 74 end 75 76 check convergence at pg_{k+1} 77 end 78 */ 79 80 static PetscErrorCode TaoSolve_BNTR(Tao tao) 81 { 82 PetscErrorCode ierr; 83 TAO_BNK *bnk = (TAO_BNK *)tao->data; 84 KSPConvergedReason ksp_reason; 85 86 PetscReal resnorm, oldTrust, prered, actred, stepNorm, steplen; 87 PetscBool stepAccepted = PETSC_TRUE, shift = PETSC_FALSE; 88 PetscInt stepType = BNK_NEWTON; 89 90 PetscFunctionBegin; 91 /* Initialize the preconditioner, KSP solver and trust radius/line search */ 92 tao->reason = TAO_CONTINUE_ITERATING; 93 ierr = TaoBNKInitialize(tao, bnk->init_type);CHKERRQ(ierr); 94 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 95 96 /* Have not converged; continue with Newton method */ 97 while (tao->reason == TAO_CONTINUE_ITERATING) { 98 99 if (stepAccepted) { 100 tao->niter++; 101 tao->ksp_its=0; 102 /* Compute the hessian and update the BFGS preconditioner at the new iterate*/ 103 ierr = TaoBNKComputeHessian(tao);CHKERRQ(ierr); 104 } 105 106 /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */ 107 ierr = TaoBNKComputeStep(tao, shift, &ksp_reason);CHKERRQ(ierr); 108 109 /* Store current solution before it changes */ 110 oldTrust = tao->trust; 111 bnk->fold = bnk->f; 112 ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr); 113 ierr = VecCopy(tao->gradient, bnk->Gold);CHKERRQ(ierr); 114 ierr = VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);CHKERRQ(ierr); 115 116 /* Temporarily accept the step and project it into the bounds */ 117 ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr); 118 ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr); 119 120 /* Check if the projection changed the step direction */ 121 ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr); 122 ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr); 123 ierr = VecNorm(tao->stepdirection, NORM_2, &stepNorm);CHKERRQ(ierr); 124 if (stepNorm != bnk->dnorm) { 125 /* Projection changed the step, so we have to recompute predicted reduction. 126 However, we deliberately do not change the step norm and the trust radius 127 in order for the safeguard to more closely mimic a piece-wise linesearch 128 along the bounds. */ 129 ierr = MatMult(bnk->H_inactive, tao->stepdirection, bnk->Xwork);CHKERRQ(ierr); 130 ierr = VecAYPX(bnk->Xwork, -0.5, bnk->G_inactive);CHKERRQ(ierr); 131 ierr = VecDot(bnk->Xwork, tao->stepdirection, &prered); 132 } else { 133 /* Step did not change, so we can just recover the pre-computed prediction */ 134 ierr = KSPCGGetObjFcn(tao->ksp, &prered);CHKERRQ(ierr); 135 } 136 prered = -prered; 137 138 /* Compute the actual reduction and update the trust radius */ 139 ierr = TaoComputeObjective(tao, tao->solution, &bnk->f);CHKERRQ(ierr); 140 actred = bnk->fold - bnk->f; 141 ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);CHKERRQ(ierr); 142 143 if (stepAccepted) { 144 /* Step is good, evaluate the gradient and the hessian */ 145 steplen = 1.0; 146 ++bnk->newt; 147 ierr = TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); 148 ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr); 149 ierr = VecNorm(tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr); 150 if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1,"User provided compute function generated Not-a-Number"); 151 } else { 152 /* Step is bad, revert old solution and re-solve with new radius*/ 153 steplen = 0.0; 154 bnk->f = bnk->fold; 155 ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr); 156 ierr = VecCopy(bnk->Gold, tao->gradient);CHKERRQ(ierr); 157 ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr); 158 if (oldTrust == tao->trust) { 159 /* Can't change the radius anymore so just terminate */ 160 tao->reason = TAO_DIVERGED_TR_REDUCTION; 161 } 162 } 163 164 /* Check for termination */ 165 ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->Gwork);CHKERRQ(ierr); 166 ierr = VecNorm(bnk->Gwork, NORM_2, &resnorm);CHKERRQ(ierr); 167 ierr = TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr); 168 ierr = TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);CHKERRQ(ierr); 169 ierr = (*tao->ops->convergencetest)(tao, tao->cnvP);CHKERRQ(ierr); 170 } 171 PetscFunctionReturn(0); 172 } 173 174 /*------------------------------------------------------------*/ 175 176 PETSC_INTERN PetscErrorCode TaoSetUp_BNTR(Tao tao) 177 { 178 TAO_BNK *bnk = (TAO_BNK *)tao->data; 179 PetscErrorCode ierr; 180 181 PetscFunctionBegin; 182 ierr = TaoSetUp_BNK(tao);CHKERRQ(ierr); 183 if (!bnk->is_nash && !bnk->is_stcg && !bnk->is_gltr) SETERRQ(PETSC_COMM_SELF,1,"Must use a trust-region CG method for KSP (KSPNASH, KSPSTCG, KSPGLTR)"); 184 PetscFunctionReturn(0); 185 } 186 187 /*------------------------------------------------------------*/ 188 189 PETSC_INTERN PetscErrorCode TaoCreate_BNTR(Tao tao) 190 { 191 TAO_BNK *bnk; 192 PetscErrorCode ierr; 193 194 PetscFunctionBegin; 195 ierr = TaoCreate_BNK(tao);CHKERRQ(ierr); 196 tao->ops->solve=TaoSolve_BNTR; 197 tao->ops->setup=TaoSetUp_BNTR; 198 199 bnk = (TAO_BNK *)tao->data; 200 bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */ 201 bnk->sval = 0.0; /* disable Hessian shifting */ 202 PetscFunctionReturn(0); 203 }