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Explores convex optimization, convex functions, and their properties, including strict convexity and strong convexity, as well as different types of convex functions like linear affine functions and norms.
Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.
Covers the fundamentals of Nonlinear Programming and its applications in Optimal Control, exploring techniques, examples, optimality definitions, and necessary conditions.
Explores primal-dual optimization methods, focusing on Lagrangian approaches and various methods like penalty, augmented Lagrangian, and splitting techniques.
Covers gradient descent methods for convex and nonconvex problems, including smooth unconstrained convex minimization, maximum likelihood estimation, and examples like ridge regression and image classification.
Covers the basics of optimization, including historical perspectives, mathematical formulations, and practical applications in decision-making problems.