The Department of Mathematics at the College of Computer Science and Mathematics held a seminar on Tuesday, 4/5/2026, titled * Mathematical Structures in Modern Optimization: From Quadratic to Conic Programming *, presented by (Dr. Hamsa Throt. Saeed, Dr. Elaf Sulaiman ).

Seminar Summary:

This session explores the evolution of optimization theory from the classical “formulaic” approach of Quadratic Programming (QP) to the “structural” paradigm of Conic Programming (CP). While quadratic models have long served as the workhorse for engineering and finance, they often struggle with numerical stability and representational limits when scaling to complex, uncertain environments.

The core of this discussion focuses on the Geometry of Cones—specifically the transformation of quadratic constraints into the Second-Order (Lorentz) Cone and the Positive Semidefinite Cone. We examine the mathematical “lifting” techniques that allow researchers to map standard quadratic forms into higher-dimensional conic spaces, thereby ensuring computational tractability and unlocking the power of modern Primal-Dual Interior-Point Methods.