Offered: Fall 2025 (current)
This course delves into advanced optimization techniques, covering a range of mathematical programming methodologies. Topics include calculus-based and constrained optimization methods, the Lagrange multiplier approach, and linear programming formulations with real-world applications. Students will explore standard and canonical forms, constraint transformations, and variable adjustments, including slack, surplus, and artificial variables. The course also introduces the Simplex Method, optimality conditions, the Big-M method, and duality in linear programming, including complementary slackness properties. Additional topics include transportation problem modeling and solutions, interior point algorithms such as Khachiyan's ellipsoid method and Karmarkar’s projective algorithm, as well as integer linear programming, quadratic programming, and nonlinear programming. Finally, the course covers dynamic programming concepts, recurrence relations, the 0-1 knapsack problem, optimal binary search trees, and minimum spanning trees.
The core objectives of this course are:
To introduce students to advanced optimization techniques and their mathematical foundations.
To explore different programming methods, including linear, nonlinear, and dynamic programming.
To develop problem-solving skills through optimization algorithms.
To analyze real-world applications of optimization in computing and engineering.
To apply theoretical optimization techniques to practical problem-solving scenarios.
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