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Lecture
Linear Programming Duality
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Linear Optimization: Auxiliary Problem
Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.
Introduction to Optimization
Covers the basics of optimization, including historical perspectives, mathematical formulations, and practical applications in decision-making problems.
Optimization Programs: Piecewise Linear Cost Functions
Covers the formulation of optimization programs for minimizing piecewise linear cost functions.
Approximation Algorithms
Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.
Linear Programming: Optimization and Constraints
Explores linear programming optimization with constraints, Dijkstra's algorithm, and LP formulations for finding feasible solutions.
Linear Programming Duality
Covers linear programming duality and complementary slackness condition.
Linear Programming Duality
Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.
Primal-dual optimization: Theory and Computation
Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.
Optimization with Constraints: KKT Conditions
Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.
Linear Optimization: Finding Initial BFS
Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.