Minicourse: Nonlinear Programming

I plan to discuss the theory of constrained nonlinear optimization. Right now, I expect to discuss the theory in Nonlinear Programming by Olvi Mangasarian, and expand it with some of the basic numerical methods from Introduction to Linear and Nonlinear Programming by David Luenberger and Introduction to Mathematical Programming by Hillier and Lieberman. The book by Mangasarian discusses

1. Linear Inequalities and Theorems of the Alternative
2. Convex Sets in Rⁿ
3. Convex and Concave Functions
4. Saddlepoint Optimality of Nonlinear Programming with Differentiability
5. Differentiable Convex and Concave Functions
6. Optimality Criteria in Nonlinear Programming with Differentiability
7. Duality in Nonlinear Programming
8. Generalizations of Convex Functions