Mathematical Optimization for Advanced Studies
Explore a comprehensive syllabus covering mathematical optimization concepts, methods, and applications for advanced studies in the field. Topics include basic concepts, line search, steepest descent, Newton methods, constrained optimization, and references to further readings.
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Presentation Transcript
Optimization Fourth Class 2020 - 2021 By ??.????? ??????? ?????? Dept. of Math. Education College for Pure Sciences ?????????? ?? ?????? Iraq
The Syllabus No. Name of Chapter 1 Basic Concepts Description Introduction, Mathematical Optimization, Basic Optimization Problem, Types of Optimization Problems, Some Mathematical Foundations, Convex Sets and Convex Functions, Optimality Conditions for Unconstrained Optimization, Structure of Optimization Problem
No. Name of Chapter Description 2 Line Search Introduction, Forward Backward Method, Convergence Theory for Exact Line Search, The Golden Section Method, Fibonacci Method, Quadratic Interpolation Method, Cubic Interpolation Method
No. Name of Chapter The Steepest Descent and Newton Methods Conjugate Direction Methods Description 3 The Steepest Descent Method, The Newton Method 4 Conjugate Directions, Conjugate Gradient Methods, Fletcher-Reeves Method, Dixon Method, Polack Method
No. Name of Chapter Quasi Newton Method Constrained Optimization Description 5 Introduction, Quasi Newton Equation, Davidon-Fletcher- Powell Method Statement of Constrained Optimization Problem, Multivariate Optimization with Equality Constraints, Lagrange Multiplier Method, Multivariate Optimization with Inequality Constraints, Kuhn Tucker Conditions 6
References 1: A Modified Conjugate Gradient Method for Unconstrained Optimization by Can Li, 2013. 2: Constrained Optimization, by Peter Kennedy, 2019. 3: Constrained Optimization, by Joshua Wild, 2013. 4: Constrained Optimization and Lagrange Multiplier Methods, by Dimitri P. Bertsekas, 1996.
5: Convex Optimization, by Stephen Boyd, and Lieven Vandenberghe, 2009. 6: Introduction to Optimization, Anand Jayant Kulkarmi, 2017. 7: Numerical Analysis and Optimization, by Gregoire Allaire, 2007. 8: Method of Quadratic Interpolation, by Keller Vandebogent, 2017. 9: Optimization Theory, by Shibayan Sarkar, 2016. 10: Optimization and Optimal Control, by Altannar Chinchuluun, 2010.
11: Optimization Theory and Methods, by Weilyu Sun, 2006. 12: Optimization Theory and Applications, by S.S.Rao, 1979. 13: Numerical Methods for Unconstrained Optimization, by M.A.Wolfe, 1977.
