Statistics 310: Optimization and Simulation
This course will consist of two five-week modules devoted
to (1) stochastic simulation and (2) continuous optimization.
Students will be expected to complete several substantial programming
projects during the course. Following is a brief synopsis:
1. Stochastic Simulation:
- importance sampling and sequential importance sampling
- MCMC (Markov chain Monte Carlo)
- perfect sampling
- particle filtering
- simulated annealing
Connections with some important problems of combinatorial optimization,
including max-flow, graph-partitioning, and matching algorithms, will also be discussed. The utility of MCMC methods will be illustrated by a number
of substantial examples, including
- simulation of self-avoiding random walks
- enumeration of contingency tables with fixed margins
- simulation of Ising models and spin glasses
2. Continuous Optimization:
- Fundamentals of Unconstrained Optimization.
- Line Search Methods
- Trust-Region Methods.
- Conjugate Gradient Methods for Unconstrained Optimization.
- Quasi-Newton Methods (if time permits).
- Calculating Derivatives, Automatic Differentiation.
- Nonlinear Equations (and, if time permits, Nonlinear Least-Square Problems).
- Theory of Constrained Optimization.
- Fundamental of Algorithms for Nonlinear Constrained Optimization.
- Interior Point Methods for Nonlinear Programming.
A. Stochastic Simulation
B. Continuous Optimization
Assignments (Stochastic Simulation):
Coded Text for Assignment 3.
TSP Itinerary for Assignment 4.
Darwin Finch Data