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This paper introduces a learning-based method for approximating parametric nonconvex optimization problems with a surrogate problem amenable to parallel convex optimization. The surrogate is constructed as the minimum of a finite set of functions composed of convex and monotonic terms, enabling efficient solution. Experiments on a nonconvex path tracking problem demonstrate the approximation quality of the proposed surrogate.
Unlock the power of parallel convex optimization for previously intractable parametric nonconvex problems using a learned surrogate.
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.