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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4047 APPLIED OPTIMIZATION ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (Evening) Mathematics (English)

Course Objective

: Introduction. Mathematical background. Optimization models.Optimization of unconstrained nonlinear single variable models. Optimization of unconstrained nonlinear multivariable models. Constarined nonlinear programming problems. Nonlinear regression. Chemical Engineering applications

Learning Outcomes of the Course Unit

1   to be able to understand the decision making procedure and the relation with the optimization 2   to have the ability to analyze the structure of the problem and to recognize the model 3   to be able to introduce the linear and nonlinear optimization models 4   to be able to solve the problem using suitable method 5   to be able to use modern techniques and equipments (computers and program packages) 6   to be able to interpret the results and to decide the optimum solution 7   to define the to be able necessary and sufficiency conditions of any optimization problem 8   to be able to find the nonlinear data analysis coefficients solving the unconstrained optimization problem

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Introduction: Main definitions, objective and general optimization problems, solution methods 2 Mathematical background: Continuity of the functions, Convex and concave functions, single and multivariable functions, convex region, necessary and sufficiency conditions for extremum 3 Optimization models: Linear and nonlinear type models, constrained and unconstrained optimization problems 4 Optimization of single unconstrained functions: Search methods (Newton, Quasi-Newton, Secant) 5 Region Elimination method (Golden Section Search), Polynomial approximation methods 6 Optimization of unconstrained nonlinear multivariable functions : Direct methods (Hooke and Jeeves, Random Search, 7 Indirect methods (with Derivative : Steepest Descent and Ascent, Davidon Fletcher-Powell) 8 Indirect methods continued: Conjugate Gradient 9 Constrained linear programming problems: Graphical Solution 10 Problems and Solution 11 Algebraic Solution (Simplex Method) 12 Constrained nonlinear programming problems: Optimum conditions for constrained problems applications 13 Lagrange multipliers and Lagrangian functions, Kuhn-Tucker conditions and its applications 14 Nonlinear Regression: Nonlinear least-squares data fitting, Solution of different models using suitable methods

Recomended or Required Reading

Textbook: G.R.Walsh, Methods of Optimization, Wiley Int. Sci., (1975) 2 Other: T.F.Edgar, D.M.Himmelblau, Optimization of Chemical Processes, McGraw-Hill, (1988) Notes

Planned Learning Activities and Teaching Methods

Lecture Notes Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

1. Attending at least 70 percent of lectures is mandatory. 2. Plagiarism of any type will result in disciplinary action

Contact Details for the Lecturer(s)

email: halil.oruc@deu.edu.tr tel: (232) 3018577 Ofis B205

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 12 5 60 Preparation for midterm exam 1 25 25 Preparation for final exam 1 30 30 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 4 3 3 3 4 4 4 4 LO.2 3 3 4 3 4 LO.3 3 4 4 4 4 LO.4 4 3 4 4 4 LO.5 3 4 5 4 4 LO.6 4 3 3 3 5 4 5 LO.7 4 3 4 4 4 LO.8 4 3 4 4 4