- Lecture 1: (From Heron of Alexandria, Dido, and Tartaglia's problems to Max-flow)
- Lecture 2: (Existence of an optimizer: Weierstrass theorem, and relaxing compactness ala coercivity)
- Lecture 3: (First-order necessary conditions of optimality: unconstrained case)
- Lecture 4: (Second-order 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 second-order conditions for convexity, and global feature of minimizers of convex functions)
- Lecture 11: (Examples: quadratic functions and log-determinant 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: Dubovitskii-Milytuin theorem)
- Lecture 18: (Euler-Lagrange 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: (Saddle-point theorem, Lagrangian duality, and primal-dual problems)
- Lecture 23: (Nonlinear programming: Karush-Kuhn-Tcuker 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 discrete-time gradient flow dynamics with constant step size)
- Lecture 28: (Convergence of discrete-time 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: (Saddle-point 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 zero-sum games)
- (Potential games)
- Lecture 34: (Project Presentations)
- (Sum Of Squares convexity))
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