Instructor:

Robert J. Vanderbei, ACE-42 E-Quad, 8-0876, rvdb@princeton.edu, http://www.princeton.edu/~rvdb/

Lectures:

MW 1:30–2:50 pm, E-415

Office Hours:

MW 4:30-6:00, ACE-42

1 Outline

• Motivating Examples.
  Structural Optimization via Finite Element Models, Trajectory Optimization, Minimal Surfaces, Antennae Array Synthesis, Digital Filter Design, Hydrothermal Power Generation.
• Duality.
  The Dual Problem, The Weak Duality Theorem, The Strong Duality Theorem, Complementary Slackness, Strict Complementarity, Lagrangian Duality.
• Path-Following Method.
  The Barrier Problem, Lagrange Multipliers, Second-Order Information, Computing Step Directions, Newton’s Method, The Barrier Parameter, Step Lengths.
• Homogeneous Self-Dual Method.
  From Standard Form to Self-Dual Form, Homogeneous Self-Dual Problems, Predictor-Corrector Algorithm, Convergence Analysis, Complexity of the Predictor-Corrector Algorithm, The KKT-System, Back to Standard Form.
• Quadratic Programming.
  The Markowitz Model, The Dual, Convexity and Complexity, Solution via Interior-Point Methods, Homogeneous Self-Dual Method.
• Convex Programming.
  Convex and Concave Functions, Problem Formulation, Solution via Interior-Point Methods.
• Non-Convex Nonlinear Programming.
  Merit Functions, Descent Directions, Local Optimality, Global Optimality.

2 Readings

Lecture material will be drawn from the following sources.

References