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Constrained Optimization solution algorithms are restricted to point basedsolutions. In practice, single or multiple objectives must be satisfied,wherein both the objective function and constraints can be non-convex resultingin multiple optimal solutions. Real world scenarios include intersectingsurfaces as Implicit Functions, Hyperspectral Unmixing and Pareto Optimalfronts. Local or global convexification is a common workaround when faced withnon-convex forms. However, such an approach is often restricted to a strictclass of functions, deviation from which results in sub-optimal solution to theoriginal problem. We present neural solutions for extracting optimal sets asapproximate manifolds, where unmodified, non-convex objectives and constraintsare defined as modeler guided, domain-informed $L_2$ loss function. Thispromotes interpretability since modelers can confirm the results against knownanalytical forms in their specific domains. We present synthetic and realisticcases to validate our approach and compare against known solvers forbench-marking in terms of accuracy and computational efficiency.

Extracting Optimal Solution Manifolds using Constrained Neural Optimization