 Lecture 1: (From Heron of Alexandria, Dido, and Tartaglia's problems to Maxflow)
 Lecture 2: (Existence of an optimizer: Weierstrass theorem, and relaxing compactness ala coercivity)
 Lecture 3: (Firstorder necessary conditions of optimality: unconstrained case)
 Lecture 4: (Secondorder necessary conditions of optimality, and spectral decomposition of symmetric matrices)
 Lecture 5: (Constrained optimization: scenarios with infeasible directions)
 Lecture 6: (Optimization constrained on lower dimensional surfaces: variations using curves)
 Lecture 7: (Affine sets, hyperplanes, and convex sets)
 Lecture 8: (Geometry of convex set and cones, Jensen's inequality, operations on convex sets and Minkowski sums)
 Lecture 9: (Convex functions, quasiconvexity, strict convexity, and epigraphs)
 Lecture 10: (First and secondorder conditions for convexity, and global feature of minimizers of convex functions)
 Lecture 11: (Examples: quadratic functions and logdeterminant function on the space of positive definite symmetric matrices)
 Lecture 12: (Variational inequality I)
 Lecture 13: (Variational inequality II, examples)
 Lecture 14: (Projection maps)
 Lecture 15: (Separation: Support hyperplane theorem)
 Lecture 16: (Separation of convex sets, strict and proper separation)
 Lecture 17: (A glimpse at duality using a separation theorem: DubovitskiiMilytuin theorem)
 Lecture 18: (EulerLagrange equation, Lagrangian mechanics, and Legendre transformation to Hamiltonian mechanics)
 Lecture 19: (Fenchel duality theorem)
 Lecture 20: (Applications of Fenchel duality theorem to resource allocation)
 Lecture 21: (von Neumann's minmax theorem through Fenchel duality)
 Lecture 22: (Saddlepoint theorem, Lagrangian duality, and primaldual problems)
 Lecture 23: (Nonlinear programming: KarushKuhnTcuker necessary conditions of optimality in the presence of inequalities)
 Lecture 24: (Nonlinear programming through duality)
 Lecture 25: (Linear programming and duality)
 Lecture 26: (Overview of some numerical methods for optimization)
 Lecture 27: (Convergence of discretetime gradient flow dynamics with constant step size)
 Lecture 28: (Convergence of discretetime gradient flow dynamics with diminishing step size)
 Lecture 29: (Convergence rates: linear, sublinear, superlinear, and quadratic)
 Lecture 30: (Newton's method, and its convergence properties: applications to least squares problem)
 Lecture 31: (Saddlepoint dynamics)
 Lecture 32: (Project Presentations)
 (Alternating Direction Method of Multipliers and regularization)
 (Linear Matrix Inequalities in systems and control)
 Lecture 33: (Project Presentations)
 (Fictitious play learning in zerosum games)
 (Potential games)
 Lecture 34: (Project Presentations)
 (Sum Of Squares convexity))
