Lectures: Mon and Wed between 12:30-13:45 at CAS B26
Instructor: Emre Mengi Office: SCI 114 E-mail: emengi@ku.edu.tr Phone: 338-1658
Teaching Assistant:
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Course Description:
Optimization problems arise in various fields ranging from economics to physics and in our daily lives. Airlines arrange their schedules to maximize their profit subject to constraints imposed by limited resources such as number of crew-members and planes. Ray of light follows a path to minimize the travel time. Two main ingredients of an optimization problem are
The first part of this course will focus on unconstrained optimization problems in the absence of constraints. Constrained optimization problems will be considered in the second part. For both cases we will derive the optimality conditions (i.e. conditions that distinguish an optimal point from an ordinary point), introduce numerical algorithms to locate points satisfying the optimality conditions and analyze the convergence properties of the numerical algorithms. (See the course syllabus for issues such as grading and the formats of the exams.) Announcements:
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Textbooks:
- Numerical Optimization – Class Notes by Philip E. Gill and Margaret H. Wright (This is the main textbook. You can obtain a copy from the Xerox room in the student center.)
- Numerical Optimization 2nd Edition by Jorge Nocedal and Stephen J. Wright (On several occasions we will also depend on this book. This book will be available at the reserve desk in the library.)
Resources:
- Lecture Notes
- Lecture 3 – Derivative of a Vector-valued Function, First Order Optimality Conditions
- Lecture 4 – Second Order Optimality Conditions
- Lecture 5 – Eigenvalue Characterization for Positive Definiteness
- Lecture 6 – Root Finding, Newton’s Method for Univariate Functions, Sequences and their Convergence
- Lecture 7 – Newton’s Method for Multivariate Functions
- Lecture 8 – Convergence of Newton’s Method
- Lecture 9 – Line Search Algorithms
- Lecture 10 – Inexact Line Search
- Lecture 11 – Modified Newton’s Method
- Lecture 12 – Quasi Newton Methods – Part I
- Lecture 13 – Quasi Newton Methods – Part II
- Lecture 14 – Convergence of Line Search Algorithms
- Lecture 15 – Nonlinear Optimization with Equality-Constraints (Part I)
- Lecture 16 – Nonlinear Optimization with Equality-Constraints (Part II)
- Lecture 17 – Nonlinear Optimization with Equality-Constraints (Part III)
- Lecture 18 – Nonlinear Optimization with Equality-Constraints (Part IV)
- Lecture 19 – Nonlinear Optimization with Inequality Constraints (Part I)
- Lecture 20 – Nonlinear Optimization with Inequality Constraints (Part II)
- Lecture 21 – Nonlinear Optimization with Inequality Constraints (Part III)
- Lectures 22,23 – Sensitivity of Constrained Optimization Problems and Duality for Linear Programs
- Lecture 24 – Primal-Dual Interior Point Methods for Linear Programs
- Lecture 25 – Practical Aspects of Primal-Dual Interior Point Methods for Linear Programs
- Lecture 26 – Penalty Function Methods for Nonlinear Programs
- Lecture 27 – Logarithmic Barrier Method
- Some Additional Examples Regarding Linear Programs and Duality
Homeworks: All homeworks are due by 14:00 on the indicated dates below.
Midterm: Final: |
Exams and Solutions:
Important Enrollment Dates and Holidays:
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