Syllabus: This is a senior/first year graduate-level course on optimization. Topics include necessary and sufficient conditions for local optima; characterization of convex sets and functions; unconstrained optimization, gradient descent and it variants; constrained optimization and the gradient projection method; optimization with equality and inequality constraints, Lagrange multipliers, KKT conditions; penalty, barrier function methods; strong and weak duality and Slater conditions; sub-gradient descent and conjugate gradient methods; proximal gradient descent; augmented Lagrangian methods; applications.
Prerequisites: Linear algebra at the level of Math 415, programming skills at the level of ECE 220.
Textbook: D. Bertsekas. Nonlinear Programming, Athena Scientific, 2016.
Other References:
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
D. Luenberger and Y. Ye. Linear and Nonlinear Programming, Springer, 2008.
Exams, homework, grading, etc.: