Parametric Nonconvex Optimization via Convex Surrogates
This work addresses optimization difficulties in engineering and machine learning by providing a more efficient solution method, though it appears incremental as it builds on existing convex optimization techniques.
The paper tackles the challenge of solving parametric nonconvex optimization problems by developing a learning-based method to construct a convex surrogate that approximates the original problem, enabling parallel convex optimization, with numerical experiments on a path tracking problem confirming its approximation quality.
This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions, given by the composition of convex and monotonic terms, so that the surrogate problem can be solved directly through parallel convex optimization. As a proof of concept, numerical experiments on a nonconvex path tracking problem confirm the approximation quality of the proposed method.