Jay Rosenberger

Tightening bilinear relaxations using geometric rotation

Categories Global Optimization, Nonlinear Optimization

A classical approach for handling non-convex optimization problems involving bilinear terms is to approximate the bilinear expressions using McCormick relaxations. Such relaxations are central to global optimization methods, with the spatial branch-and-bound (sBB) algorithm being one of the most widely used approaches. In the spatial branching step, the algorithm partitions the feasible region using axis-aligned … Read more

Lipschitz Based Lower Bound Construction for Surrogate Optimization

Categories Bound-constrained Optimization, Global Optimization, Global Optimization Applications Tags , , ,

Bounds play a vital role in guiding optimization algorithms by enhancing convergence, improving solution quality, and quantifying optimality gaps. While Lipschitz-based lower bounds are well-established, their effectiveness is often constrained by the function’s topological properties. To address these limitations, we propose an approach that integrates nonlinear distance metrics with surrogate approximations, yielding more adaptive and … Read more