Learning to Solve Optimization Problems With Hard Linear Constraints

Constrained optimization problems have appeared in a wide variety of challenging real-world problems, where constraints often capture the physics underlying system. Classic methods for solving these relied on iterative algorithms that explored feasible domain search best solution. These became computational bottleneck decision-making and adversely impacted time-sensitive applications. Recently, neural approximators shown promise as replacement solvers can output optimal solution single feed-forward providing rapid solutions to problems. However, enforcing through networks remains an open challenge. In this paper, we developed approximator maps inputs problem with hard linear is nearly optimal. Our proposed approach consists five main steps: 1) reducing original set independent variables, 2) finding gauge function $\ell _{\infty} $ -norm unit ball reduced problem, 3) learning optimization’s virtual point ball, 4) mapping project onto space, then 5) values dependent variables from variable recover problem. We guarantee feasibility sequence steps. Unlike current learning-assisted solutions, our method free parameter-tuning (compared penalty-based methods) removes iterations altogether. demonstrated performance quadratic programming context power dispatch (critical resiliency electric grid) constrained non-convex image registration results supported theoretical findings demonstrate superior terms time, optimality, compared existing approaches.