BICEP: Bi-linear algorithm for composite empirical likelihood

Run TRICEP/BICEP for a vector mean.

TRICEP_mean(beta_test, X, F_reparam = NULL, s_hat_reparam = NULL,
  prox_fun = NULL, detect_outlier = F, q = NULL, reuse_delta = F,
  prox_fun_arg = list(), wts_init = NULL, vary_penalty = c("RB", "RB2",
  "none"), RB_mu = 10, RB_tau = 2, RB2_ksi = 2, outer_eps = 1e-08,
  outer_rel_eps = 1e-04, dual_step = 2, outer_maxit = 1000,
  wts_beta_rep = 1, outer_tol_type = c("primal_dual", "fval", "primal"),
  outlier_loop_arg = optim_outlier_control(),
  mirror_arg = optim_mirror_control(line_search = T),
  prox_optim_arg = optim_prox_control(), verbose = F)

`beta_test`	a vector of candidate test values.
`X`	a design matrix with observations in rows and variables in columns.
`F_reparam`	the `F` matrix for the affine reparameterization.
`s_hat_reparam`	the `s` vector for the affine reparameterization.
`prox_fun`	a proximal operator. This should be an `R` object.
`detect_outlier`	a boolean indicating whether an REL update should be run to detect outliers.
`q`	the number of detected outliers (only valid if `detect_outlier = T`). The default is `floor(.05 * n)`.
`reuse_delta`	use the last estimate of `delta` in the current outer loop iteration.
`prox_fun_arg`	a list of arguments passed to `prox_fun`.
`wts_init`	an initial guess for the weights vector. Default is `1/n`.
`vary_penalty`	a string specifying the type of penalty variation.
`RB_mu`	the `mu` parameter for the residual balancing scheme.
`RB_tau`	the `tau` parameter for the residual balancing scheme.
`RB2_ksi`	the `ksi` parameter for the `RB2` scheme.
`outer_eps`	absolute tolerance required for outer loop convergence.
`outer_rel_eps`	relative tolerance required for outer loop convergence.
`dual_step`	initial penalty parameter.
`outer_maxit`	maximum number of outer loop iterations.
`wts_beta_rep`	the number of repetitions of the block coordinate descent update within each outer loop iteration.
`outer_tol_type`	the type of tolerance check for the outer loop.
`outlier_loop_arg`	control arguments passed to the `delta` optimization; see `optim_outlier_control`.
`mirror_arg`	control arguments passed to the mirror descent optimization; see `optim_mirror_control`.
`prox_optim_arg`	a list of control arguments passed to the proximal gradient descent update for `prox_fun`; see `optim_prox_control`.
`verbose`	a boolean to allow console output.