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R-package ic.infer implements estimation and (likelihood ratio) testing for normal distribution situations with inequality constraints. Constrained estimation is implemented using R-package quadprog, and implementation of hypothesis tests makes use of multivariate normal probabilities calculated by R-package mvtnorm.
Order-restricted estimation of linear models takes the unconstrained linear model as the starting point. The default output includes several overall likelihood ratio tests, and - if requested - bootstrap confidence intervals for the restricted parameters. There is also a function that enables averaging over R2-values for order-restricted linear models (which, however, takes distinctly longer than calculation of the metric lmg using the function calc.relimp available in R-package relaimpo for unrestricted linear models).