Actual source code: ssls.h

petsc-3.15.0 2021-04-05
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```  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

32:  The theory for the feasible version follows from the feasible descent
33:  algorithm framework.

35:  References:
36:    Billups, "Algorithms for Complementarity Problems and Generalized
37:      Equations," Ph.D thesis, University of Wisconsin - Madison, 1995.
38:    De Luca, Facchinei, Kanzow, "A Semismooth Equation Approach to the
39:      Solution of Nonlinear Complementarity Problems," Mathematical
40:      Programming, 75, pages 407-439, 1996.
41:    Ferris, Kanzow, Munson, "Feasible Descent Algorithms for Mixed
42:      Complementarity Problems," Mathematical Programming, 86,
43:      pages 475-497, 1999.
44:    Fischer, "A Special Newton-type Optimization Method," Optimization,
45:      24, pages 269-284, 1992
46:    Munson, Facchinei, Ferris, Fischer, Kanzow, "The Semismooth Algorithm
47:      for Large Scale Complementarity Problems," Technical Report 99-06,
48:      University of Wisconsin - Madison, 1999.
49: */

51: #ifndef __TAO_SSLS_H
53: #include <petsc/private/taoimpl.h>

55: typedef struct {
56:   Vec ff;       /* fischer function */
57:   Vec dpsi;     /* gradient of psi */

59:   Vec da;       /* work vector for subdifferential calculation (diag pert) */
60:   Vec db;       /* work vector for subdifferential calculation (row scale) */
61:   Vec dm;   /* work vector for subdifferential calculation (mu vector) */
62:   Vec dxfree;

64:   Vec t1;       /* work vector */
65:   Vec t2;       /* work vector */

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

69:   PetscReal merit; /* merit function value (norm(fischer)) */
70:   PetscReal merit_eqn;
71:   PetscReal merit_mu;

73:   PetscReal delta;
74:   PetscReal rho;

76:   PetscReal rtol;       /* Solution tolerances */
77:   PetscReal atol;

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

81:   /* Interior-point method data */
82:   PetscReal mu_init; /* initial smoothing parameter value */
83:   PetscReal mu;      /* smoothing parameter */
84:   PetscReal dmu;     /* direction in smoothing parameter */
85:   PetscReal mucon;   /* smoothing parameter constraint */
86:   PetscReal d_mucon; /* derivative of smoothing constraint with respect to mu */
87:   PetscReal g_mucon; /* gradient of merit function with respect to mu */

89:   Mat J_sub, Jpre_sub; /* subset of jacobian */
90:   Vec f;        /* constraint function */

92:   IS fixed;
93:   IS free;
94: } TAO_SSLS;

96: PetscErrorCode TaoSetFromOptions_SSLS(PetscOptionItems *,Tao);
97: PetscErrorCode TaoView_SSLS(Tao,PetscViewer);

99: PetscErrorCode Tao_SSLS_Function(TaoLineSearch, Vec, PetscReal *, void *);
100: PetscErrorCode Tao_SSLS_FunctionGradient(TaoLineSearch, Vec, PetscReal *, Vec, void *);

102: #endif

```