Theory and algorithms for nonlinearly constrained optimization. Relevant geometric concepts, including tangent and normal cones, theorems of the alternative, and separation results. Constraint qualifications. Geometric and algebraic expression of first-order optimality conditions. Second-order optimality conditions. Duality. Nonlinear programming algorithms: Merit functions and filters; interior-point, augmented Lagrangian, and sequential quadratic programming algorithms. Prereq: CS 726 or equivalent or consent of instructor.