Optimal Decision Making: Sensitivity Analysis

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Local Sensitivity Analysis: Feasibility and Optimality

Explores local sensitivity analysis in linear programming, examining how changes impact optimality and feasibility.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Linear Programming Duality

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Certificates: Existence and Proving

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

Convex Optimization Problems: Theory and Applications

Explores convex optimization problems, optimality criteria, equivalent problems, and practical applications in transportation and robotics.

Nonlinear Programming: Part I

Covers the fundamentals of Nonlinear Programming and its applications in Optimal Control, exploring techniques, examples, optimality definitions, and necessary conditions.

Branch & Bound: Optimization

Covers the Branch & Bound algorithm for efficient exploration of feasible solutions and discusses LP relaxation, portfolio optimization, Nonlinear Programming, and various optimization problems.

Duality: Economic Interpretation

Explores duality in linear programming, strong duality, complementary slackness, and the economic interpretation of dual variables as prices.

Semi-Definite Programming

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