xref: /petsc/src/tao/leastsquares/impls/brgn/brgn.h (revision b27f53d5f5b22630ba5fcad3f213a141cee9e1d9)

/*
Context for Bounded Regularized Gauss-Newton algorithm.
Extended with L1-regularizer with a linear transformation matrix D:
0.5*||Ax-b||^2 + lambda*||D*x||_1
When D is an identity matrix, we have the classic lasso, aka basis pursuit denoising in compressive sensing problem.
*/

#pragma once

#include <../src/tao/bound/impls/bnk/bnk.h> /* BNLS, a sub-type of BNK, is used in brgn solver */
#include <petsc/private/taoimpl.h>

#define BRGN_REGULARIZATION_USER   0
#define BRGN_REGULARIZATION_L2PROX 1
#define BRGN_REGULARIZATION_L2PURE 2
#define BRGN_REGULARIZATION_L1DICT 3
#define BRGN_REGULARIZATION_LM     4
#define BRGN_REGULARIZATION_TYPES  5

typedef struct {
  PetscErrorCode (*regularizerobjandgrad)(Tao, Vec, PetscReal *, Vec, void *);
  PetscErrorCode (*regularizerhessian)(Tao, Vec, Mat, void *);
  void                     *reg_obj_ctx;
  void                     *reg_hess_ctx;
  Mat                       H, Hreg, D;                             /* Hessian, Hessian for regulization part, and Dictionary matrix have size N*N, and K*N respectively. (Jacobian M*N not used here) */
  Vec                       x_old, x_work, r_work, diag, y, y_work; /* x, r=J*x, and y=D*x have size N, M, and K respectively. */
  Vec                       damping;                                /* Optional diagonal damping matrix. */
  Tao                       subsolver, parent;
  PetscReal                 lambda, epsilon, fc_old;                      /* lambda is regularizer weight for both L2-norm Gaussian-Newton and L1-norm, ||x||_1 is approximated with sum(sqrt(x.^2+epsilon^2)-epsilon)*/
  PetscReal                 downhill_lambda_change, uphill_lambda_change; /* With the lm regularizer lambda diag(J^T J),
                                                                 lambda = downhill_lambda_change * lambda on steps that decrease the objective.
                                                                 lambda = uphill_lambda_change * lambda on steps that increase the objective. */
  TaoBRGNRegularizationType reg_type;
  PetscBool                 mat_explicit;
} TAO_BRGN;