Introduction to Optimization

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Simplex Algorithm: Solution on a Vertex

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

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Two-phase Simplex Algorithm: Introduction and Duality

Introduces the two-phase simplex algorithm and explores duality in linear programming.

Optimization: Mathematical Principles and Algorithms

Covers mathematical principles and algorithms of optimization, using real-world examples and Python implementation.

Optimization with Constraints: KKT Conditions

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

Hedging for LPs

Covers the concept of hedging for Linear Programs and the simplex method, focusing on minimizing costs and finding optimal solutions.

Discrete Optimization: Relaxation

Explores solving discrete optimization problems by relaxing integrality constraints.

Linear Programming: Solving LPs

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

Relations Between Events

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

Nonlinear Optimization Methods

Covers methods for solving nonlinear optimization problems, including direct search, Newton-Raphson, and branch and bound.