I am trying to solve an optimization problem with a quadratic objective function and non-linear constraints, using SQP (Sequential Quadratic Programming). I am attempting at doing the implementation in R. However, the R algorithm require initial values, that must satisfy the constraints.
I am not sure how can I easily determine an initial value for $y$ that satisfies both constraints. Here is the optimization problem:
Note that $b$ is a known vector, $c$ is a known constant, and $A^+$ is the Moore-Penrose inverse of known matrix $A$.
Any help would be appreciated. If some sample/mock data is required, please let me know.
Thank you!