Optimization

Linear Programming

1. Linear Programsformulation, geometry of feasibility, standard form4–8.5 h
2. Simplex Methodtableau, pivoting, degeneracy, two-phase method4–8.5 h
3. Dualitydual problems, complementary slackness, sensitivity analysis4–8.5 h

Nonlinear & Convex Optimization

1. Convex Sets & Functionsconvexity, Jensen, epigraphs4–8.5 h
2. Convex Optimization Problemsconic, geometric programming, semidefinite programming intro4–8.5 h
3. KKT ConditionsLagrange multipliers generalization, constrained optimization4–8.5 h
4. Optimization Algorithmsgradient descent, Newton's method, interior point methods, subgradient4–8.5 h

Applications

1. Least Squares & Regressionnormal equations, ridge regression, regularization4–8.5 h
2. Combinatorial Optimization Introinteger programming, NP-hardness, relaxations4–8.5 h
3. Duality in Economicsshadow prices, resource valuation4–8.5 h