Optimization, Convex Analysis, and Geometric Structures

The CIMPA school offers a comprehensive and advanced curriculum focused on optimization, mathematical programming, and their applications across various fields. The courses delve into both theoretical foundations and practical methodologies, covering topics such as nonsmooth optimization, integer linear programming, linear optimization, separation theorems, dynamic optimization, and monotone operator theory. Students will explore key concepts like subdifferentials, branch-and-bound methods, Fourier elimination, Pontryaguin's principle, and maximal monotonicity, while gaining hands-on experience with numerical methods and computational tools. The program emphasizes the interplay between theory and real-world applications, equipping students with the skills to tackle complex optimization problems in areas such as combinatorial optimization, optimal control, convex and nonconvex analysis, and variational inequalities. Through a blend of rigorous theoretical training and practical problem-solving, the school prepares participants for cutting-edge research and innovative solutions in mathematics and its interdisciplinary applications.