Most linear program packages can solve such problems. But it might become very trivial and time-consuming to really make them run in the format of your problem. If your original loss function  is sum of squares or some common convex one, then it won't be too hard to solve manually. Just Lagrange method.

施加非线性约束得到受约束回归模型，该模型必需采用非线性最小二乘法（nonlinear least squares）进行估计。
nls(formula, data,control）其中formula和data用法和最小二乘一样，control添加约束。具体如何添加请参考nls（）帮助文档