Lectures related to Linear Constraints and Vertices

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Covers optimization problems in path finding and portfolio allocation.

Explores convex sets, their properties, and applications in optimization.

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.

Explores basic solutions in linear constraints and the equivalence with vertices.

Explains linear constraints and the concept of a polyhedron in optimization problems.

Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.

Covers classical optimization problems, brute force algorithms, and integer linear optimization.

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

Covers linear constraints and degeneracy in polyhedrons, focusing on basic solutions and degenerate cases.

Covers the transhipment problem, optimal solutions, and total unimodularity in matrices.

Covers the basics of linear programming and the simplex method, focusing on finding optimal solutions and handling degeneracy.

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

Explores the design process of pavilion structures, emphasizing the creation of a topological polyhedron as the foundation document.

Explains the simplex algorithm process of finding the next vertex and selecting variables.

Covers single inequality or equality constraints and necessary optimality conditions in optimization problems.

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Explores solving strategies for energy system optimization problems and different types of optimization approaches.