The text introduces students to numerous methods in solving a variety of Optimization problems. Also, the narrow focus of most math textbooks is completely dedicated to nonlinear programming, linear programming, combinatorial or convex optimization.
The text introduces students to numerous methods in solving a variety of Optimization problems. Also, the narrow focus of most math textbooks is completely dedicated to nonlinear programming, linear programming, combinatorial or convex optimization.
Jeffrey Paul Wheeler earned his PhD in Combinatorial Number Theory from the University of Memphis by extending what had been a conjecture of Erd¿s on the integers to finite groups. He has published, given talks at numerous schools, and twice been a guest of Trinity College at the University of Cambridge. He has taught mathematics at Miami University (Ohio), the University of Tennessee-Knoxville, the University of Memphis, Rhodes College, the University of Pittsburgh, Carnegie Mellon University, and Duquesne University. He has received numerous teaching awards and is currently in the Department of Mathematics at the University of Pittsburgh. He also occasionally teaches for Pitt's Computer Science Department and the College of Business Administration. Dr. Wheeler's Optimization course was one of the original thirty to participate in the Mathematical Association of America's NSF-funded PIC Math program.
Inhaltsangabe
1. 1. Preamble. 2. The Language of Optimization. 3. Computational Complexity. 4. Algebra Review. 5. Matrix Factorization. 6. Linear Programming. 7. Sensitivity Analysis. 8. Integer Linear Programing. 9. Calculus Review. 10. A Calculus Approach to Nonlinear Programming. 11. Constrained Nonlinear Programming: Lagrange Multipliers and the KKT Conditions. 12. Optimization involving Quadratic Forms. 13. Iterative Methods. 14. Derivative-Free Methods. 15. Search Algorithms. 16. Important Sets for Optimization. 17. The Fundamental Theorem of Linear Programming. 18. Convex Functions. 19. Convex Optimization. 20. An Introduction to Combinatorics. 21. An Introduction to Graph Theory. 22. Network Flows. 23. Minimum-Weight Spanning Trees and Shortest Paths. 24. Network Modeling and the Transshipment Problem. 25. The Traveling Salesperson Problem. Probability. 27. Regression Analysis via Least Squares. 28. Forecasting. 29. Introduction to Machine Learning.
1. 1. Preamble. 2. The Language of Optimization. 3. Computational Complexity. 4. Algebra Review. 5. Matrix Factorization. 6. Linear Programming. 7. Sensitivity Analysis. 8. Integer Linear Programing. 9. Calculus Review. 10. A Calculus Approach to Nonlinear Programming. 11. Constrained Nonlinear Programming: Lagrange Multipliers and the KKT Conditions. 12. Optimization involving Quadratic Forms. 13. Iterative Methods. 14. Derivative-Free Methods. 15. Search Algorithms. 16. Important Sets for Optimization. 17. The Fundamental Theorem of Linear Programming. 18. Convex Functions. 19. Convex Optimization. 20. An Introduction to Combinatorics. 21. An Introduction to Graph Theory. 22. Network Flows. 23. Minimum-Weight Spanning Trees and Shortest Paths. 24. Network Modeling and the Transshipment Problem. 25. The Traveling Salesperson Problem. Probability. 27. Regression Analysis via Least Squares. 28. Forecasting. 29. Introduction to Machine Learning.
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