Type:	Package
Title:	Linear Programming via Regularized Least Squares
Version:	0.1.0
Description:	The Linear Programming via Regularized Least Squares (LPPinv) is a two-stage estimation method that reformulates linear programs as structured least-squares problems. Based on the Convex Least Squares Programming (CLSP) framework, LPPinv solves linear inequality, equality, and bound constraints by (1) constructing a canonical constraint system and computing a pseudoinverse projection, followed by (2) a convex-programming correction stage to refine the solution under additional regularization (e.g., Lasso, Ridge, or Elastic Net). LPPinv is intended for underdetermined and ill-posed linear problems, for which standard solvers fail.
License:	MIT + file LICENSE
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.2)
Imports:	rclsp
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
URL:	https://github.com/econcz/rlppinv
BugReports:	https://github.com/econcz/rlppinv/issues
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2025-11-28 01:13:20 UTC; ilyabolotov
Author:	Ilya Bolotov [aut, cre]
Maintainer:	Ilya Bolotov <ilya.bolotov@vse.cz>
Repository:	CRAN
Date/Publication:	2025-12-03 20:30:13 UTC

Solve a linear program via Convex Least Squares Programming (CLSP).

Description

Solve a linear program via Convex Least Squares Programming (CLSP).

Usage

lppinv(
  c = NULL,
  A_ub = NULL,
  b_ub = NULL,
  A_eq = NULL,
  b_eq = NULL,
  non_negative = TRUE,
  bounds = NULL,
  replace_value = NA_real_,
  tolerance = sqrt(.Machine$double.eps),
  final = TRUE,
  alpha = NULL,
  ...
)

Arguments

Value

An object of class "clsp" containing the fitted CLSP model.

See Also

clsp

CVXR-package

Examples

  ## Linear Programming via Regularized Least Squares (LPPinv)
  ## Underdetermined and potentially infeasible LP system

  set.seed(123456789)

  # sample (dataset)
  A_ub <- matrix(rnorm(50 * 500), nrow = 50, ncol = 500)
  A_eq <- matrix(rnorm(25 * 500), nrow = 25, ncol = 500)
  b_ub <- matrix(rnorm(50),       ncol = 1)
  b_eq <- matrix(rnorm(25),       ncol = 1)

  # model (no default non-negativity, unique MNBLUE solution)
  model <- lppinv(
      A_ub = A_ub,
      A_eq = A_eq,
      b_ub = b_ub,
      b_eq = b_eq,
      non_negative = FALSE,
      final = TRUE,
      alpha = 1.0                                   # unique MNBLUE estimator
  )

  # coefficients
  print("x hat (x_M hat):")
  print(round(model$x, 4))

  # numerical stability (if available)
  if (!is.null(model$kappaC)) {
      cat("\nNumerical stability:\n")
      cat("  kappaC :", round(model$kappaC, 4), "\n")
  }
  if (!is.null(model$kappaB)) {
      cat("  kappaB :", round(model$kappaB, 4), "\n")
  }
  if (!is.null(model$kappaA)) {
      cat("  kappaA :", round(model$kappaA, 4), "\n")
  }

  # goodness-of-fit diagnostics (if available)
  if (!is.null(model$nrmse)) {
      cat("\nGoodness-of-fit:\n")
      cat("  NRMSE :", round(model$nrmse, 6), "\n")
  }
  if (!is.null(model$x_lower)) {
      cat("  Diagnostic band (min):", round(min(model$x_lower), 4), "\n")
  }
  if (!is.null(model$x_upper)) {
      cat("  Diagnostic band (max):", round(max(model$x_upper), 4), "\n")
  }

  # bootstrap NRMSE t-test (if supported by rclsp)
  if ("ttest" %in% names(model)) {
      cat("\nBootstrap t-test:\n")
      tt <- model$ttest(sample_size = 30,
                        seed = 123456789,
                        distribution = "normal")
      for (nm in names(tt)) {
          cat("   ", nm, ": ", round(tt[[nm]], 6), "\n", sep = "")
      }
  }