1 /* 2 Context for Bounded Regularized Gauss-Newton algorithm. 3 Extended with L1-regularizer with a linear transformation matrix D: 4 0.5*||Ax-b||^2 + lambda*||D*x||_1 5 When D is an identity matrix, we have the classic lasso, aka basis pursuit denoising in compressive sensing problem. 6 */ 7 8 #if !defined(__TAO_BRGN_H) 9 #define __TAO_BRGN_H 10 11 #include <../src/tao/bound/impls/bnk/bnk.h> /* BNLS, a sub-type of BNK, is used in brgn solver */ 12 13 typedef struct { 14 PetscErrorCode (*regularizerobjandgrad)(Tao, Vec, PetscReal *, Vec, void *); 15 PetscErrorCode (*regularizerhessian)(Tao, Vec, Mat, void *); 16 void *reg_obj_ctx; 17 void *reg_hess_ctx; 18 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) */ 19 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. */ 20 Vec damping; /* Optional diagonal damping matrix. */ 21 Tao subsolver, parent; 22 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)*/ 23 PetscReal downhill_lambda_change, uphill_lambda_change; /* With the lm regularizer lambda diag(J^T J), 24 lambda = downhill_lambda_change * lambda on steps that decrease the objective. 25 lambda = uphill_lambda_change * lambda on steps that increase the objective. */ 26 PetscInt reg_type; 27 PetscBool mat_explicit; 28 } TAO_BRGN; 29 30 #endif /* if !defined(__TAO_BRGN_H) */ 31