Linear (Integer) Programming
- Some definitions: Degeneracy, Total unimodularity, Shadow price, Reduced Cost, Sensitivity analysis, minkowski theorem
- Primal and dual simplex methods
- Big-M, Two phase methods
- Theory of simplex method
- Duality
- Fundemental problems and their mathematical formulations: matching, assignment, shortest path, maximum flow
- Linear programming modeling tips: absolute value, etc.
- Integer programming modeling tips: m constraints among n constraints, etc.
- Decomposition methods: Dantzig-Wolfe, Bender’s
Nonlinear Programming
- Some definitions: Convex set, convex function
- Optimality conditions
- Newton’s and secant methods
- Positive definite matrices
- Steepest descent
- Geometric programming
- Duality (Lagrangean)
Probability & Statistics
- Some definitions: Bayes theorem, Maximum likelihood, Exponential family, Canonical parametrization, Expectation, Variance, Law of large numbers, Central limit theorem
- Basic dicrete probability distributions: Bernoulli, Binomial, Multinomial, etc.
- Basic continous probability distributions: Normal, Poisson, Beta, Gamma, etc.
- Bayesian aproach vs Frequentist aproach
- Condition probability
- Hypothesis testing
- ANOVA
Stochastic Processes
- State transition modeling
- Birth-death processes
- Poisson processes
- Queuing theory
- Markov chains
- Renewal-Reward processes
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