Mathematical Optimization
Department of Mathematical Sciences
WORCESTER POLYTECHNIC INSTITUTE
MA 4325, Mathematical Optimization, Term D04
B. Doytchinov
Office: SH105D
Office hours: TBA
e-mail:bogdand@wpi.edu
TEXT
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Dimitri Bertsekas, Nonlinear Programming,
Athena Scientific; 2nd edition (September 1999).
COURSE CONTENTS
The course consists of six main parts:
- Unconstrained Optimization.
Optimality Conditions, gradient methods, Newton and
Quasi-Newton methods, disrete-time optimal control.
Chapter 1.
- Convex Optimization.
Conditional gradient method, gradient projection
methods, manifold suboptimization.
Chapter 2.
- Lagrange Multipliers - Theory.
Necessary and sufficient conditions for equality
constraints, inequality constaraints, linear constraints
and duality.
Chapter 3.
- Lagrange Multiplieers - Algorithms.
Barrier and interior point methods, penalties,
Lagrangian and primal-dual interior point methods.
Chapter 4.
- Duality and Convex Programming.
Duality, convex cost, conjugate functions, Fenchel
duality, discrete optimization.
Chapter 5.
- Dual methods.
Dual ascent methods, nondiferentiable optimization,
decomposition methods.
Chapter 6.
CLASSES
There are four lectures per week, conducted in
SH203, on Mo,Tu,Th, and Fr, 1:00 - 1:50pm.
You are supposed to attend all lectures. If you
miss a class, it is your responsibility to make a copy of the classnotes
from another student and make sure you learn what you have missed.
HOMEWORK
There will be four or five homework assignments throughout the course.
You will have approximately one weak to complete each assignment. The
problems will be taken most often from the book. Each assignment will
be announced in class, and then it will also appear
on the web.
SOFTWARE
Some of the problems assigned might be computationally intensive. You will
need some computing device and software which permits rudimentary programming.
For example, MATLAB and Maple can be used successfully in most cases.
A programmable calculator can be too slow for purposes of number-crunching.
GRADING POLICY
There will be a take-home Mid-Term Exam, and also a Final Exam
the form of which will be determined later. Your final grade will be
calculated in the following way:
30% of the grade come from the Homework,
30% of the grade come from the Midterm Exam,
40% of the grade come from the Final Exam.
These scores are combined to give a final number of
points, between 0 and 100. The
point ranges for the final grades should be expected to be:
A: 100-90
B: 89-80
C: 79-65
MA 4235, Mathematical Optimization, Term D03
Send me mail:
bogdand@wpi.edu
