SHAPE

SHAPE's advantage is interpreted as coming mainly from fixed-budget navigation rather than terminal convergence alone. SHAPE uses an event-stage optimizer composed of a slow planner and a fast local port-Hamiltonian controller. SHAPE treats fixed-budget nonconvex optimization as a two-timescale phase-space navigation problem. SHAPE lifts optimizer state from position alone to position and momentum-like coordinates. At each stage, SHAPE's planner outputs a mode, anchor, structural gain modifiers, anchor strength, and a horizon or budget. SHAPE was implemented in PyTorch and trained on a single NVIDIA A100 for functional benchmarks.