Exact methods: Branch and Bound

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Integer Programs: Optimization and Constraints

Explores integer programs, nonconvex optimization, constraints, and geometric aspects of linear programming for optimal solutions.

Linear Programming: Extreme Points

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

Simplex Algorithm: Solution on a Vertex

Explores the simplex algorithm and how optimal solutions can be found on vertices of constraint polyhedra.

Relations Between Events

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

The Transhipment Problem: Total Unimodularity

Covers the transhipment problem, the incidence matrix, and total unimodularity.

Introduction to Optimization

Covers the basics of optimization, including historical perspectives, mathematical formulations, and practical applications in decision-making problems.

Branch & Bound Algorithm: LP Based Approach

Explores the LP-based Branch & Bound algorithm for finding optimal solutions.

Linear Programming: Solving LPs

Covers the process of solving Linear Programs (LPs) using the simplex method.

Simplex Algorithm: Graphical Method

Illustrates the simplex algorithm through a graphical method to find optimal solutions.

Linear Programming: Two-phase Simplex Algorithm

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.