Smoothening max-terms and analytical minimization of half-perimeter wirelength

This work addresses a class of optimization problems arising in engineering, where the objective function contains non-differentiabilities, and yet needs to be minimized analytically. While large classes of non-differentiabilities can be successfully smoothened by approximations, existing techniques fail to provide a symmetric, smooth and computationally convenient approximation for the multivariate max function with provable properties. Our work proposes such an approximation and immediately applies it to a hypergraph placement problem, previously addressed by heuristic transformation of hypergraphs into graphs. Empirical validation is performed by comparing our implementations to several optimal but unacceptably laborious methods, including network flows and linear programming with CPLEX.