Course Information

Course Name	Turkish	Hesaplamalı Optimizasyon
	English	Computational Optimization
Course Code	MAT 351E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	3	3	-	-
Course Language		English
Course Coordinator		Ersin Özuğurlu
Course Objectives		1- To teach the modeling and graphical solution of the optimization problems. 2- To teach the necessary and sufficient conditions for the local and global minimization. 3- To teach the methods of solutions of the single and multivariable functions in the unconstrained problems. 4- To teach the quadratic programming, penalty and barrier methods for the constrained optimization problems. 5- To teach the Simplex method for the solution of linear constrained optimization problems. 6- To show computer applications with up-to-date programing languages for the optimization problems.
Course Description		Problem formulation in optimization and their graphical solutions. Unconstrained Optimization; conditions for local minima. Line Search Methods; Golden Section method, Newton’s method. Multi Variable Problems; steepest descent method and scaling, conjugate gradient methods: The Fletcher and Reeves Method, Modified Newton Method, Marquardt Modification, Quasi-Newton methods: Davidon Fletcher Powel (DFP) method, Broyden Fletcher Goldfarb Shanno (BFGS) method. Least squares method, Trust-region methods. Linear and Nonlinear Constrained Optimization Problems; Lagrange multipliers, Kuhn-Tucker conditions, Sensitivity analysis, Quadratic programming, Penalty and Barrier methods, Simplex method.
Course Outcomes		I. Formulate the optimization problems, II. Solve the optimization problems by graphical methods, III. Apply basic numerical algorithms about the minimization of the single and multivariable functions in the unconstrained optimization problems and to analyze and interpret their results. IV. Solve the nonlinear constrained optimization problems in terms of penalty and barrier methods, V. Solve the quadratic optimization problems, VI. Solve the linear constrained optimization problems in terms of Simplex method, VII. Use computer for the solutions of optimization problems, VIII. Use the necessary and sufficient conditions of the local and global minimization, IX. Apply the Least squares method, Trust-region method.
Pre-requisite(s)		MAT143 and MAT287
Required Facilities		MATLAB
Other
Textbook		J. S. Arora, “Introduction to Optimum Design”, McGraw-Hill Book Company, 1989
Other References		1) J. Nocedal and S. J. Wright: Numerical Optimization, second ed. Springer Verlag, 2006, ISBN D-387-30303-0 2) M. S. Bazaraa, H.D. Sherali, C. M. Shetty “Nonlinear Programming: Theory and Algorithms”, John Willeys & Song, New York, 1993. 3) P. Venkataraman, “Applied Optimization with MATLAB Programming”, John Wiley & Sons, New York., 2002. 4) M. S. Bazaraa, J.J. Jarvis, H.D. Sherali, “Linear Programming and Network Flows”, John Willeys & Song, New York, 1990.

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