CIMPA 2026:

The CIMPA School on Optimization, Convex Analysis, and Geometric Structures is scheduled to be held at two institutions: COMSATS University Islamabad (CUI) Lahore Campus for the first nine days, and the University of Management and Technology (UMT) for the final five days.

In this CIMPA School, we will cover a range of advanced topics central to modern optimization and mathematical analysis. The first three days of the school are devoted to covering the foundational concepts of the topics to ensure that all participants are well-prepared for the advanced material. The course on Numerical Non smooth Optimization will introduce students to sub gradient methods, hybrid techniques, and smoothing strategies for both convex and nonconvex problems, along with real-life applications. We will explore Monotone Operator Theory, a powerful tool in variational inequalities and convex optimization, focusing on maximal monotone operators and their applications. Through lectures on Separation Theorems and Duality in Optimization, participants will gain insights into supporting hyperplanes, duality gaps, and generalized derivatives, essential in solving complex optimization problems. The school will also delve into the geometry of Voronoi Diagrams, including higher-order and farthest diagrams, and their role in geometric tessellations. Additionally, we will examine the theory of Evenly Convex Sets, providing extensions to classical convexity concepts and Motzkin's decomposition theorem. Finally, the course on Optimal Control Theory will cover dynamic optimization, Pontryagin's principle, and techniques to stabilize and control dynamic systems. These topics together will equip students with a deep understanding of the interplay between optimization, convex analysis, and geometric structures.

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