Ontological Foundations of Convex Optimization, Duality, and Extremum Convergence in the 4D Bicone-Frustum Cosmos

Key Points

• The aim is to establish that convex optimization and related concepts arise from cosmic geometry rather than being purely theoretical.
• Utilized the PFUS framework for analysis.
• Explored the 45° coaxial bicone ontology for understanding geometric implications.
• Demonstrated relationships between primal and dual optimization through cosmic structures.
• Convex optimization is associated with the lower cone of the bicone structure.
• Dual concave optimization is linked to the upper cone.
• Strong duality and closure are represented by the frustum.