Lectures related to Linear Constraints: Basic Solutions

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

Covers the 2D case of polynomial encroaching and vertices of polyhedra.

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

Explores relations between events, disjunctive constraints, and modeling with binary variables in optimization problems.

Explores the cutset formulation for the MST Problem and Gomory Cutting Planes method.

Covers exercises on the Simplex Algorithm, optimizing solutions subject to linear constraints.

Explores certificates, proving solution existence, constraints, and linear programming duality.

Covers the concepts of faces, facets, and vertices in polyhedra, exploring minimal faces and inequalities.

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.