Introduction to network-based data analysis with focus on cluster detection and clustering using clique relaxations. Examples of network models of various complex systems; a systematic framework for cluster analysis based on network representation; exact and approximate algorithms for optimal cluster detection problems; continuous global optimization approaches.
Credits: 1 Lecture Hour.
Prerequisite: Instructor's approval.
Basics of deterministic optimization with focus on modeling and computer solutions; practical examples to develop understanding of modeling and solution techniques that can be used to improve decision-making; linear, non-linear, mixed integer, combinatorial and network optimization problems.
Credits: 1.5 Lecture Hours.
Prerequisite: Graduate classification; ENGY majors.
Theory and numerical methods for deterministic linear and nonlinear optimization; topics include linear programming, unconstrained-nonlinear optimization, constrained-nonlinear optimization, Lagrange and K-K-T conditions, and numerical algorithms.
Credits: 3 Lecture Hours.
Focus on heuristic optimization methods that search beyond local optima; includes neighborhood search methods and advanced search strategies such as genetic algorithms, simulated annealing, neural networks, tabu search, and greedy randomized adaptive search procedures.
Credits: 3 Lecture Hours.
Prerequisite: ISEN 620 or ISEN 622 or approval of instructor.
Development of the mathematics and algorithms associated with linear programming; convex sets and cones, polyhedral sets, duality theory, sensitivity analysis, simplex, revised simplex and dual simplex methods; also covered are bounded variables, column generation, decomposition, integer programming; computer assignment.
Credits: 3 Lecture Hours.
Prerequisite: MATH 304.
Understanding of algorithms for nonlinear optimatization; development of optimality conditions and different types of algorithms for unconstrained and constrained problems; formulation and solution of many types of discrete dynamic programming problems
Credits: 3 Lecture Hours.
Prerequisite: MATH 304.
Fundamental theory, mathematical modeling, and algorithms of network flow models including shortest path models maximum flow and cost minimization models; out-of-kilter algorithm; pure and generalized network specializations of the primal simplex method; introduction to multi-commodity networks.
Credits: 3 Lecture Hours.
Formulation principles and general approaches for solving integer (and mixed, integer linear) programs including preprocessing, cutting plane methods, branch and bound, branch and cut, branch and price, and Lagrange relaxation; classical problem structures with special-purpose solution algorithms; fundamental theory of polyhedra, methods to generate valid inequalities and computational complexity.
Credits: 3 Lecture Hours.
Principles of economic equivalence; time value of money; analysis of single and multiple investments; comparison of alternatives; capital recovery and after-tax analysis of economic projects.
Credits: 2 Lecture Hours.
Development and application of fundamental deterministic optimization models and solution methods; focus on quantitative modeling and formulation of linear, integer, and network flow problems; use of computer optimization software to model and solve real-life problems.
Credits: 3 Lecture Hours.