Lecture

Linear Inequalities and Equivalent LP

Related lectures (29)

Linear Programming: Extreme Points

Explores extreme points in linear programming and the role of constraints in finding optimal solutions.

Linear Programming Basics

Covers the basics of linear programming, defining corners, extreme points, and feasible solutions within polyhedrons.

Closest Vector Problem: Voronoi Cells

Explores the closest vector problem in lattices and the role of Voronoi cells in determining the closest vector.

Linear Algebra Review: Vector Spaces and Matrix Operations

Offers a quick review of key linear algebra concepts essential for further topics.

Convex Polyhedra and Linear Programs

Explores convex polyhedra, linear programs, and their optimization importance.

Linear Algebra: Efficiency and Complexity

Explores constraints, efficiency, and complexity in linear algebra, emphasizing convexity and worst-case complexity in algorithm analysis.

Optimization Algorithms

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Linear Dependence of Vectors

Explores linear dependence of vectors, demonstrating examples and conditions for collinearity.

Game Theory: Minimax Theorem

Explores zero-sum games and the minimax theorem in Game Theory, emphasizing optimal strategies.

Partial Differential Equations

Covers the basics of Partial Differential Equations, including the Laplace equation, heat equation, and wave equation.

Linear Programming Duality

Explores the concept of duality in linear programming and its practical implications in optimization.

Branch and Bound: Heuristic Maximization

Explains the Branch and Bound algorithm for heuristic maximization problems using LP relaxations and pruning techniques.

Integer Programming Basics

Introduces the basics of integer programming, including binary integer programs and constraint strategies.

Linear Equations: Vectors and Matrices

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Pseudorandomness: Theory and Applications

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Building Ramanujan Graphs

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Partial Differential Equations and Hessians

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.

Ramanujan Graphs: Constructions and Similarities

Explores Ramanujan graphs' constructions, matching polynomials, perfect matchings, and universal covers, along with quantitation and qualitative aspects.

Linear Algebra: Identical Applications

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.