Nonlinear Programming

Course Description

6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems.

Technical Requirements

Special software is required to use some of the files in this course:.fortran.

Lecture Notes

LEC #
TOPICS
1
Introduction (PDF)
2
Unconstrained Optimization - Optimality Conditions (PDF)
3
Gradient Methods (PDF)
4
Convergence Analysis of Gradient Methods (PDF)
5
Rate of Convergence (PDF)
6
Newton and Gauss - Newton Methods (PDF)
7
Additional Methods (PDF)
8
Optimization Over a Convex Set; Optimality Conditions (PDF)
9
Feasible Direction Methods (PDF)
10
Alternatives to Gradient Projection (PDF)
11
Constrained Optimization; Lagrange Multipliers (PDF)
12
Constrained Optimization; Lagrange Multipliers (PDF)
13
Inequality Constraints (PDF)
14
Introduction to Duality (PDF)
15
Interior Point Methods (PDF)
16
Penalty Methods (PDF)
17
Augmented Lagrangian Methods (PDF)
18
Duality Theory (PDF)
19
Duality Theorems (PDF)
20
Strong Duality (PDF)
21
Dual Computational Methods (PDF)
22
Additional Dual Methods (PDF)

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