Linear Constraints: Elimination of Variables

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

Linear Optimization: Fundamentals

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

Introduction to Optimization

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

Linear Constraints: Polyhedron

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

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Two Inequalities and Feasible Cone: Linearized Approach

Explains feasible directions, linearized cone, and Constraint Qualification conditions in optimization.

The Trouble with Quadratic Penalties: ALM as a Fix

Explores the challenges of quadratic penalties in optimization and the use of Augmented Lagrangian Methods (ALM) as a solution.

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

ALM with Inequalities: Next Steps in Optimization

Explores the Augmented Lagrangian Method with equality and inequality constraints in optimization, emphasizing the importance of slack variables.

Optimization Problems: Lagrange Multiplier Equations

Introduces the Lagrange multiplier method for solving optimization problems with constraints.