Date: 2025-03-28T21:11:15+00:00

Actual source code: ssls.h

      1: /* Context for SSXLS
      2:    -- semismooth (SS) - function not differentiable
      3:                       - merit function continuously differentiable
      4:                       - Fischer-Burmeister reformulation of complementarity
      5:                         - Billups composition for two finite bounds
      6:    -- infeasible (I)  - iterates not guaranteed to remain within bounds
      7:    -- feasible (F)    - iterates guaranteed to remain within bounds
      8:    -- linesearch (LS) - Armijo rule on direction

     10:  Many other reformulations are possible and combinations of
     11:  feasible/infeasible and linesearch/trust region are possible.

     13:  Basic theory
     14:    Fischer-Burmeister reformulation is semismooth with a continuously
     15:    differentiable merit function and strongly semismooth if the F has
     16:    lipschitz continuous derivatives.

     18:    Every accumulation point generated by the algorithm is a stationary
     19:    point for the merit function.  Stationary points of the merit function
     20:    are solutions of the complementarity problem if
     21:      a.  the stationary point has a BD-regular subdifferential, or
     22:      b.  the Schur complement F'/F'_ff is a P_0-matrix where ff is the
     23:          index set corresponding to the free variables.

     25:    If one of the accumulation points has a BD-regular subdifferential then
     26:      a.  the entire sequence converges to this accumulation point at
     27:          a local q-superlinear rate
     28:      b.  if in addition the reformulation is strongly semismooth near
     29:          this accumulation point, then the algorithm converges at a
     30:          local q-quadratic rate.

     32:  The theory for the feasible version follows from the feasible descent
     33:  algorithm framework. See {cite}`billups:algorithms`, {cite}`deluca.facchinei.ea:semismooth`,
     34:   {cite}`ferris.kanzow.ea:feasible`, {cite}`fischer:special`, and {cite}`munson.facchinei.ea:semismooth`.
     35: */

     37: #pragma once
     38: #include <petsc/private/taoimpl.h>

     40: typedef struct {
     41:   Vec ff;   /* fischer function */
     42:   Vec dpsi; /* gradient of psi */

     44:   Vec da; /* work vector for subdifferential calculation (diag pert) */
     45:   Vec db; /* work vector for subdifferential calculation (row scale) */
     46:   Vec dm; /* work vector for subdifferential calculation (mu vector) */
     47:   Vec dxfree;

     49:   Vec t1; /* work vector */
     50:   Vec t2; /* work vector */

     52:   Vec r1, r2, r3, w; /* work vectors */

     54:   PetscReal merit; /* merit function value (norm(fischer)) */
     55:   PetscReal merit_eqn;
     56:   PetscReal merit_mu;

     58:   PetscReal delta;
     59:   PetscReal rho;

     61:   PetscReal rtol; /* Solution tolerances */
     62:   PetscReal atol;

     64:   PetscReal identifier; /* Active-set identification */

     66:   /* Interior-point method data */
     67:   PetscReal mu_init; /* initial smoothing parameter value */
     68:   PetscReal mu;      /* smoothing parameter */
     69:   PetscReal dmu;     /* direction in smoothing parameter */
     70:   PetscReal mucon;   /* smoothing parameter constraint */
     71:   PetscReal d_mucon; /* derivative of smoothing constraint with respect to mu */
     72:   PetscReal g_mucon; /* gradient of merit function with respect to mu */

     74:   Mat J_sub, Jpre_sub; /* subset of jacobian */
     75:   Vec f;               /* constraint function */

     77:   IS fixed;
     78:   IS free;
     79: } TAO_SSLS;

     81: PetscErrorCode TaoSetFromOptions_SSLS(Tao, PetscOptionItems *);
     82: PetscErrorCode TaoView_SSLS(Tao, PetscViewer);

     84: PetscErrorCode Tao_SSLS_Function(TaoLineSearch, Vec, PetscReal *, void *);
     85: PetscErrorCode Tao_SSLS_FunctionGradient(TaoLineSearch, Vec, PetscReal *, Vec, void *);