Syllabus Application
IE 601
Optimization Theory
Faculty
Faculty of Engineering and Natural Sciences
Semester
Spring 2025-2026
Course
IE 601 -
Optimization Theory
Time/Place
Time
Week Day
Place
Date
09:40-10:30
Tue
FENS-L027
Feb 16-May 22, 2026
13:40-15:30
Thu
FENS-L067
Feb 16-May 22, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
( IE 501) or ( IE 501)
Corequisites
-
Course Type
Lecture
Instructor(s) Information
Burak Kocuk
- Email: burakkocuk@sabanciuniv.edu
Course Information
Catalog Course Description
Convex optimization and functional analysis; theory of duality; iterative methods and convergence proofs; interior point methods for linear programming; computational complexity of mathematical programming problems; extensions of linear programming.
Course Learning Outcomes:
| 1. | Understand the relationship between linear programming, convex programing and conic programming |
|---|---|
| 2. | Understand the theoretical foundation of conic programming |
| 3. | Learn applications of conic programming in engineering optimization and nonconvex optimization |
| 4. | Learn interior point methods and computational complexity of linear programming |
Course Objective
This course will cover five main topics:
1. Background Material: Basic convex analysis (convex sets, convex functions, regular cones), linear programming (polyhedral representability, duality, Farkas Lemma), convex programming (duality, optimality conditions).
2. Conic Programming Theory: Duality, tractable conic programs (second-order cone programming, semidefinite programming), conic representability, other useful cones (exponential cone, power cone).
3. Conic Programming Applications: Conic programming relaxations of non-convex optimization problems, applications in robust optimization, portfolio optimization, power systems optimization, statistics/machine learning.
4. Complexity: Computational complexity of linear programming, interior-point methods.
5. Advanced Topics: Sum-of-squares/moment relaxations for polynomial optimization problems, copositive programming (if time permits).
-
1. Background Material: Basic convex analysis (convex sets, convex functions, regular cones), linear programming (polyhedral representability, duality, Farkas Lemma), convex programming (duality, optimality conditions).
2. Conic Programming Theory: Duality, tractable conic programs (second-order cone programming, semidefinite programming), conic representability, other useful cones (exponential cone, power cone).
3. Conic Programming Applications: Conic programming relaxations of non-convex optimization problems, applications in robust optimization, portfolio optimization, power systems optimization, statistics/machine learning.
4. Complexity: Computational complexity of linear programming, interior-point methods.
5. Advanced Topics: Sum-of-squares/moment relaxations for polynomial optimization problems, copositive programming (if time permits).
Course Materials
Resources:
Lectures on Modern Convex Optimization, A. Ben-Tal and A. Nemirovski (SIAM).
Convex Optimization, S. Boyd and L. Vandenberghe (Cambridge University Press).
Numerical Optimization, J. Nocedal and S. Wright (Springer Press).
Convex Optimization, S. Boyd and L. Vandenberghe (Cambridge University Press).
Numerical Optimization, J. Nocedal and S. Wright (Springer Press).
Technology Requirements:
A Python-based modeling system for convex optimization called CVXPY will be used for the examples discussed in class and homework assignments. Please install CVXPY from https://www.cvxpy.org/.
You are also recommended to install the conic programming solver MOSEK and use
it in conjunction with CVXPY. The details can be found from https://www.cvxpy.org/install/index.html.
You are also recommended to install the conic programming solver MOSEK and use
it in conjunction with CVXPY. The details can be found from https://www.cvxpy.org/install/index.html.