Convex Optimization: Farkas' Lemma

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Convex Optimization: Dual Cones

Explores dual cones, generalized inequalities, SDP duality, and KKT conditions in convex optimization.

Optimization with Constraints: KKT Conditions

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

Convex Polyhedra and Linear Programs

Explores convex polyhedra, linear programs, and their optimization importance.

Optimal Decision Analysis

Explores strong duality, complementary slackness, economic interpretation, and stochastic problem scenarios in linear programming.

Convex Optimization: Duality and KKT Conditions

Explores convex optimization duality, KKT conditions, and financial arbitrage detection.

Linear Programming Duality

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

Linear Optimization: Auxiliary Problem

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

Introduction to Optimization

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

Optimal Decision Making: Duality

Delves into duality in optimization, weak duality, cost certificates, and transforming non-linear programs into linear ones.

Convex Optimization: Exercises

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.