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 #pragma once 9 10 #include <../src/tao/bound/impls/bnk/bnk.h> /* BNLS, a sub-type of BNK, is used in brgn solver */ 11 12 #define BRGN_REGULARIZATION_USER 0 13 #define BRGN_REGULARIZATION_L2PROX 1 14 #define BRGN_REGULARIZATION_L2PURE 2 15 #define BRGN_REGULARIZATION_L1DICT 3 16 #define BRGN_REGULARIZATION_LM 4 17 #define BRGN_REGULARIZATION_TYPES 5 18 19 typedef struct { 20 PetscErrorCode (*regularizerobjandgrad)(Tao, Vec, PetscReal *, Vec, void *); 21 PetscErrorCode (*regularizerhessian)(Tao, Vec, Mat, void *); 22 void *reg_obj_ctx; 23 void *reg_hess_ctx; 24 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) */ 25 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. */ 26 Vec damping; /* Optional diagonal damping matrix. */ 27 Tao subsolver, parent; 28 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)*/ 29 PetscReal downhill_lambda_change, uphill_lambda_change; /* With the lm regularizer lambda diag(J^T J), 30 lambda = downhill_lambda_change * lambda on steps that decrease the objective. 31 lambda = uphill_lambda_change * lambda on steps that increase the objective. */ 32 PetscInt reg_type; 33 PetscBool mat_explicit; 34 } TAO_BRGN; 35