Date: 2026-06-01T23:13:47+00:00

Actual source code: neldermead.c

      1: #include <../src/tao/unconstrained/impls/neldermead/neldermead.h>
      2: #include <petscvec.h>

      4: static PetscErrorCode NelderMeadSort(TAO_NelderMead *nm)
      5: {
      6:   PetscReal *values  = nm->f_values;
      7:   PetscInt  *indices = nm->indices;
      8:   PetscInt   dim     = nm->N + 1;
      9:   PetscInt   i, j, index;
     10:   PetscReal  val;

     12:   PetscFunctionBegin;
     13:   for (i = 1; i < dim; i++) {
     14:     index = indices[i];
     15:     val   = values[index];
     16:     for (j = i - 1; j >= 0 && values[indices[j]] > val; j--) indices[j + 1] = indices[j];
     17:     indices[j + 1] = index;
     18:   }
     19:   PetscFunctionReturn(PETSC_SUCCESS);
     20: }

     22: static PetscErrorCode NelderMeadReplace(TAO_NelderMead *nm, PetscInt index, Vec Xmu, PetscReal f)
     23: {
     24:   PetscFunctionBegin;
     25:   /*  Add new vector's fraction of average */
     26:   PetscCall(VecAXPY(nm->Xbar, nm->oneOverN, Xmu));
     27:   PetscCall(VecCopy(Xmu, nm->simplex[index]));
     28:   nm->f_values[index] = f;

     30:   PetscCall(NelderMeadSort(nm));

     32:   /*  Subtract last vector from average */
     33:   PetscCall(VecAXPY(nm->Xbar, -nm->oneOverN, nm->simplex[nm->indices[nm->N]]));
     34:   PetscFunctionReturn(PETSC_SUCCESS);
     35: }

     37: static PetscErrorCode TaoSetUp_NM(Tao tao)
     38: {
     39:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
     40:   PetscInt        n;

     42:   PetscFunctionBegin;
     43:   PetscCall(VecGetSize(tao->solution, &n));
     44:   nm->N        = n;
     45:   nm->oneOverN = 1.0 / n;
     46:   PetscCall(VecDuplicateVecs(tao->solution, nm->N + 1, &nm->simplex));
     47:   PetscCall(PetscMalloc1(nm->N + 1, &nm->f_values));
     48:   PetscCall(PetscMalloc1(nm->N + 1, &nm->indices));
     49:   PetscCall(VecDuplicate(tao->solution, &nm->Xbar));
     50:   PetscCall(VecDuplicate(tao->solution, &nm->Xmur));
     51:   PetscCall(VecDuplicate(tao->solution, &nm->Xmue));
     52:   PetscCall(VecDuplicate(tao->solution, &nm->Xmuc));

     54:   tao->gradient = NULL;
     55:   tao->step     = 0;
     56:   PetscFunctionReturn(PETSC_SUCCESS);
     57: }

     59: static PetscErrorCode TaoDestroy_NM(Tao tao)
     60: {
     61:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;

     63:   PetscFunctionBegin;
     64:   if (tao->setupcalled) {
     65:     PetscCall(VecDestroyVecs(nm->N + 1, &nm->simplex));
     66:     PetscCall(VecDestroy(&nm->Xmuc));
     67:     PetscCall(VecDestroy(&nm->Xmue));
     68:     PetscCall(VecDestroy(&nm->Xmur));
     69:     PetscCall(VecDestroy(&nm->Xbar));
     70:   }
     71:   PetscCall(PetscFree(nm->indices));
     72:   PetscCall(PetscFree(nm->f_values));
     73:   PetscCall(PetscFree(tao->data));
     74:   PetscFunctionReturn(PETSC_SUCCESS);
     75: }

     77: static PetscErrorCode TaoSetFromOptions_NM(Tao tao, PetscOptionItems PetscOptionsObject)
     78: {
     79:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;

     81:   PetscFunctionBegin;
     82:   PetscOptionsHeadBegin(PetscOptionsObject, "Nelder-Mead options");
     83:   PetscCall(PetscOptionsDeprecated("-tao_nm_lamda", "-tao_nm_lambda", "3.18.4", NULL));
     84:   PetscCall(PetscOptionsReal("-tao_nm_lambda", "initial step length", "", nm->lambda, &nm->lambda, NULL));
     85:   PetscCall(PetscOptionsReal("-tao_nm_mu", "mu", "", nm->mu_oc, &nm->mu_oc, NULL));
     86:   nm->mu_ic = -nm->mu_oc;
     87:   nm->mu_r  = nm->mu_oc * 2.0;
     88:   nm->mu_e  = nm->mu_oc * 4.0;
     89:   PetscOptionsHeadEnd();
     90:   PetscFunctionReturn(PETSC_SUCCESS);
     91: }

     93: static PetscErrorCode TaoView_NM(Tao tao, PetscViewer viewer)
     94: {
     95:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
     96:   PetscBool       isascii;

     98:   PetscFunctionBegin;
     99:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    100:   if (isascii) {
    101:     PetscCall(PetscViewerASCIIPushTab(viewer));
    102:     PetscCall(PetscViewerASCIIPrintf(viewer, "expansions: %" PetscInt_FMT "\n", nm->nexpand));
    103:     PetscCall(PetscViewerASCIIPrintf(viewer, "reflections: %" PetscInt_FMT "\n", nm->nreflect));
    104:     PetscCall(PetscViewerASCIIPrintf(viewer, "inside contractions: %" PetscInt_FMT "\n", nm->nincontract));
    105:     PetscCall(PetscViewerASCIIPrintf(viewer, "outside contractionss: %" PetscInt_FMT "\n", nm->noutcontract));
    106:     PetscCall(PetscViewerASCIIPrintf(viewer, "Shrink steps: %" PetscInt_FMT "\n", nm->nshrink));
    107:     PetscCall(PetscViewerASCIIPopTab(viewer));
    108:   }
    109:   PetscFunctionReturn(PETSC_SUCCESS);
    110: }

    112: static PetscErrorCode TaoSolve_NM(Tao tao)
    113: {
    114:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
    115:   PetscReal      *x;
    116:   PetscInt        i;
    117:   Vec             Xmur = nm->Xmur, Xmue = nm->Xmue, Xmuc = nm->Xmuc, Xbar = nm->Xbar;
    118:   PetscReal       fr, fe, fc;
    119:   PetscInt        shrink;
    120:   PetscInt        low, high;

    122:   PetscFunctionBegin;
    123:   nm->nshrink      = 0;
    124:   nm->nreflect     = 0;
    125:   nm->nincontract  = 0;
    126:   nm->noutcontract = 0;
    127:   nm->nexpand      = 0;

    129:   if (tao->XL || tao->XU || tao->ops->computebounds) PetscCall(PetscInfo(tao, "WARNING: Variable bounds have been set but will be ignored by NelderMead algorithm\n"));

    131:   PetscCall(VecCopy(tao->solution, nm->simplex[0]));
    132:   PetscCall(TaoComputeObjective(tao, nm->simplex[0], &nm->f_values[0]));
    133:   nm->indices[0] = 0;
    134:   for (i = 1; i < nm->N + 1; i++) {
    135:     PetscCall(VecCopy(tao->solution, nm->simplex[i]));
    136:     PetscCall(VecGetOwnershipRange(nm->simplex[i], &low, &high));
    137:     if (i - 1 >= low && i - 1 < high) {
    138:       PetscCall(VecGetArray(nm->simplex[i], &x));
    139:       x[i - 1 - low] += nm->lambda;
    140:       PetscCall(VecRestoreArray(nm->simplex[i], &x));
    141:     }

    143:     PetscCall(TaoComputeObjective(tao, nm->simplex[i], &nm->f_values[i]));
    144:     nm->indices[i] = i;
    145:   }

    147:   /*  Xbar  = (Sum of all simplex vectors - worst vector)/N */
    148:   PetscCall(NelderMeadSort(nm));
    149:   PetscCall(VecSet(Xbar, 0.0));
    150:   for (i = 0; i < nm->N; i++) PetscCall(VecAXPY(Xbar, 1.0, nm->simplex[nm->indices[i]]));
    151:   PetscCall(VecScale(Xbar, nm->oneOverN));
    152:   tao->reason = TAO_CONTINUE_ITERATING;
    153:   while (1) {
    154:     /* Call general purpose update function */
    155:     PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
    156:     ++tao->niter;
    157:     shrink = 0;
    158:     PetscCall(VecCopy(nm->simplex[nm->indices[0]], tao->solution));
    159:     PetscCall(TaoLogConvergenceHistory(tao, nm->f_values[nm->indices[0]], nm->f_values[nm->indices[nm->N]] - nm->f_values[nm->indices[0]], 0.0, tao->ksp_its));
    160:     PetscCall(TaoMonitor(tao, tao->niter, nm->f_values[nm->indices[0]], nm->f_values[nm->indices[nm->N]] - nm->f_values[nm->indices[0]], 0.0, 1.0));
    161:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    162:     if (tao->reason != TAO_CONTINUE_ITERATING) break;

    164:     /* x(mu) = (1 + mu)Xbar - mu*X_N+1 */
    165:     PetscCall(VecAXPBYPCZ(Xmur, 1 + nm->mu_r, -nm->mu_r, 0, Xbar, nm->simplex[nm->indices[nm->N]]));
    166:     PetscCall(TaoComputeObjective(tao, Xmur, &fr));

    168:     if (nm->f_values[nm->indices[0]] <= fr && fr < nm->f_values[nm->indices[nm->N - 1]]) {
    169:       /*  reflect */
    170:       nm->nreflect++;
    171:       PetscCall(PetscInfo(0, "Reflect\n"));
    172:       PetscCall(NelderMeadReplace(nm, nm->indices[nm->N], Xmur, fr));
    173:     } else if (fr < nm->f_values[nm->indices[0]]) {
    174:       /*  expand */
    175:       nm->nexpand++;
    176:       PetscCall(PetscInfo(0, "Expand\n"));
    177:       PetscCall(VecAXPBYPCZ(Xmue, 1 + nm->mu_e, -nm->mu_e, 0, Xbar, nm->simplex[nm->indices[nm->N]]));
    178:       PetscCall(TaoComputeObjective(tao, Xmue, &fe));
    179:       if (fe < fr) {
    180:         PetscCall(NelderMeadReplace(nm, nm->indices[nm->N], Xmue, fe));
    181:       } else {
    182:         PetscCall(NelderMeadReplace(nm, nm->indices[nm->N], Xmur, fr));
    183:       }
    184:     } else if (nm->f_values[nm->indices[nm->N - 1]] <= fr && fr < nm->f_values[nm->indices[nm->N]]) {
    185:       /* outside contraction */
    186:       nm->noutcontract++;
    187:       PetscCall(PetscInfo(0, "Outside Contraction\n"));
    188:       PetscCall(VecAXPBYPCZ(Xmuc, 1 + nm->mu_oc, -nm->mu_oc, 0, Xbar, nm->simplex[nm->indices[nm->N]]));

    190:       PetscCall(TaoComputeObjective(tao, Xmuc, &fc));
    191:       if (fc <= fr) PetscCall(NelderMeadReplace(nm, nm->indices[nm->N], Xmuc, fc));
    192:       else shrink = 1;
    193:     } else {
    194:       /* inside contraction */
    195:       nm->nincontract++;
    196:       PetscCall(PetscInfo(0, "Inside Contraction\n"));
    197:       PetscCall(VecAXPBYPCZ(Xmuc, 1 + nm->mu_ic, -nm->mu_ic, 0, Xbar, nm->simplex[nm->indices[nm->N]]));
    198:       PetscCall(TaoComputeObjective(tao, Xmuc, &fc));
    199:       if (fc < nm->f_values[nm->indices[nm->N]]) PetscCall(NelderMeadReplace(nm, nm->indices[nm->N], Xmuc, fc));
    200:       else shrink = 1;
    201:     }

    203:     if (shrink) {
    204:       nm->nshrink++;
    205:       PetscCall(PetscInfo(0, "Shrink\n"));

    207:       for (i = 1; i < nm->N + 1; i++) {
    208:         PetscCall(VecAXPBY(nm->simplex[nm->indices[i]], 1.5, -0.5, nm->simplex[nm->indices[0]]));
    209:         PetscCall(TaoComputeObjective(tao, nm->simplex[nm->indices[i]], &nm->f_values[nm->indices[i]]));
    210:       }
    211:       PetscCall(VecAXPBY(Xbar, 1.5 * nm->oneOverN, -0.5, nm->simplex[nm->indices[0]]));

    213:       /*  Add last vector's fraction of average */
    214:       PetscCall(VecAXPY(Xbar, nm->oneOverN, nm->simplex[nm->indices[nm->N]]));
    215:       PetscCall(NelderMeadSort(nm));
    216:       /*  Subtract new last vector from average */
    217:       PetscCall(VecAXPY(Xbar, -nm->oneOverN, nm->simplex[nm->indices[nm->N]]));
    218:     }
    219:   }
    220:   PetscFunctionReturn(PETSC_SUCCESS);
    221: }

    223: /*MC
    224:  TAONM - Nelder-Mead solver for derivative free, unconstrained minimization

    226:  Options Database Keys:
    227: + -tao_nm_lambda - initial step length
    228: - -tao_nm_mu     - expansion/contraction factor

    230:  Level: beginner

    232: .seealso: `Tao`, `TAONLS`, `TAONTL`, `TaoType`, `TaoCreate()`
    233: M*/

    235: PETSC_EXTERN PetscErrorCode TaoCreate_NM(Tao tao)
    236: {
    237:   TAO_NelderMead *nm;

    239:   PetscFunctionBegin;
    240:   PetscCall(PetscNew(&nm));
    241:   tao->data = (void *)nm;

    243:   tao->ops->setup          = TaoSetUp_NM;
    244:   tao->ops->solve          = TaoSolve_NM;
    245:   tao->ops->view           = TaoView_NM;
    246:   tao->ops->setfromoptions = TaoSetFromOptions_NM;
    247:   tao->ops->destroy        = TaoDestroy_NM;

    249:   /* Override default settings (unless already changed) */
    250:   PetscCall(TaoParametersInitialize(tao));
    251:   PetscObjectParameterSetDefault(tao, max_it, 2000);
    252:   PetscObjectParameterSetDefault(tao, max_funcs, 4000);

    254:   nm->simplex = NULL;
    255:   nm->lambda  = 1;

    257:   nm->mu_ic = -0.5;
    258:   nm->mu_oc = 0.5;
    259:   nm->mu_r  = 1.0;
    260:   nm->mu_e  = 2.0;
    261:   PetscFunctionReturn(PETSC_SUCCESS);
    262: }