Constrained decision-making problems are pervasive across various disciplines.

Thus, any advancements in segmentation and localization algorithm are automatically transferred to the performance of high level tasks (17).

Empirical risk minimization (ERM) is a crucial framework that offers a general approach to handling a broad range of machine learning tasks.

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraintsislarge.

Our method is able to routinely handle large data-sets with more than 7,000 sample points and outperform heuristics methods and other MIP based techniques.