Intro
 Optimization in Sciences and Engineering: Running Examples (fluid mechanics, bio, energy systems)
 Examples of formulations, flavors: discretecontinuous, convexnonconvex, multiobjective, stochastic, chanceconstrained, multilevel (e.g. games), function –> functionals (functions of functions)= calculus of variations
 What does solving optimization problem mean? Complexity. Exact vs Approximate. Analytic, automatic, numerical.
Convex Optimization (continuous)
 Examples – Linear, Quadratic, Geometric, Semidefinite
 Duality, change of variables, transformations and other tricks
 Methods of solutions (main ideas), how to use it in nonconvex world (link to next section)
 Link to discrete optimization studies (in the “statistics” portion)
Nonconvex Optimization
 find local solution, count local solutions, feasibility
 convexification/approximations (regularizations) – examples.
 change of variables … other tricks, examples
More complex optimization problems
 Robust and Stochastic Optimizations  formulations, methods of solutions
 Optimization of functionals = Calculus of variations. Example: optimization over paths.
Bonus
 Lyapunov function and stability: conditions of stability, examples of Lyapunov functions , more on dynamical systems, Hamiltonian systems, ODEs, linear systems, linearization
 Optimal Control. BellmanHamiltonJacobi. Dynamic Programming. LinearQuadraticGaussian control problems.
