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  Graduate School–New Brunswick 2010–2012 Programs, Faculty, and Courses Operations Research 711 Graduate Courses  

Graduate Courses

16:711:513 (S) Discrete Optimization (3) Develops the mathematical foundation of linear and nonlinear optimization procedures for problems in which the variables can take on values only in a finite set, usually (0,1). A variety of algorithms are presented, along with numerous applications. Boros. Prerequisite: 16:198:521 or equivalent.
16:711:514 (S) Operations Research Approaches to Data Mining (3) Mathematical programming for classification and clustering; optimization methods in feature selection; applications of semidefinite programming for dimensionality reduction such as sparse principal component analysis; a Boolean approach to rough sets and data mining; logical analysis of data; robust regression; L1-norm approximation; separating and supporting hyperplanes. Jeong. Prerequisites: Linear programming, multivariate statistics.
16:711:517 (F) Computational Projects in Operations Research (3) Individual and group assignments; intensive computer practice; coding; and programming. Boros, Staff. Prerequisite: 01:640:350 or 354.
16:711:525 (S) Stochastic Models of Operations Research (3) Overview of stochastic operations research model construction. Elements of queuing theory. Stochastic models of inventory and production control; reliability models; models in stochastic and dynamic programming; stochastic simulation and its use in operations research. Avi-Itzhak, Prekopa. Prerequisite: 01:640:477 or 16:960:654.
16:711:530 (S) Semidefinite and Second Order Cone Programming (3) Theory, algorithms, and applications of semidefinite and second order optimization problems; duality; complementarity; interior point algorithms; eigenvalue optimization; nonnegative polynomials; sum-of-square functional systems; applications in combinatorial optimization; control theory; and statistics. Alizadeh. Prerequisites: Linear algebra, Ph.D. standing.
16:711:531 (F) Actuarial Mathematics (3) Economics of insurance, life tables, life insurance, life annuities, benefit premiums and reserves, multiple-life theory, multiple-decrement models, risk theory, and population theory. Prekopa. Prerequisite: 01:960:381.
16:711:547 (S) Case Studies in Applied Operations Research (3) Applications in operations research. Investigates the modeling process as it deals with economic uncertainties, missing information, risk, and priorities. Case study approach used, with students writing "recommendation to management" reports. Guest lecturers from industry describe actual projects. Prerequisites: Linear programming, probability, and computer programming.
16:711:548 (S) Topics in Applied Operations Research (3) An introduction to the practice of operations research, illustrated by models of resource management, epidemics, vaccinations, tomography, ranking, cryptography, Fourier analysis and sampling, filtering, SVD decomposition, and others. Ben-Israel. Prerequisites: Vector calculus, linear algebra, probability; knowledge of differential equations desirable.
16:711:550 (S) Nonlinear Optimization (3) Convex sets and functions, separation. Tangent cones, multifunctions, stability. Optimality conditions, Lagrangian duality, sensitivity. Unconstrained optimization methods, rate of convergence. Penalty, dual, augmented Langrangian methods. Newton's method for constrained problems. Applications I statistics, engineering, and finance. Ruszczynski. Prerequisites: Four semesters of calculus, linear algebra.   
16:711:553 (F) Theory of Boolean Functions (3) Theory, algorithms, and applications of Boolean functions. Representations, satisfiability, and generations. Monotone, regular, threshold, quadratic, and Horn functions. Applications in OR, artificial intelligence, machine learning, and database theory. Boros. Prerequisites: Ph.D. standing; knowledge of linear algebra and combinatorics.
16:711:554 (S) Pseudo-Boolean Optimization (3) Theory, algorithms, and applications of pseudo-Boolean functions. Unconstrained binary optimization, standard linearization, local optimality, basic algorithm, graph theoretical equivalents, quadratization, theory of nonnegative quadratic polynomials, bounds, and approximations. Boros. Prerequisites: Ph.D. standing; knowledge of linear algebra and linear programming.
16:711:555 (F) Convex Analysis and Optimization (3) Finite-dimensional convex sets, cones, and functions. Separation, polarity, subgradients, and normality. Subdifferential calculus, conjugate functions, monotone operators, and bifunction duality theory. Proximal and bundle methods for optimization. Eckstein. Prerequisites: Fundamentals of real analysis, linear algebra, and multivariable calculus.
16:711:556 (S) Queuing Theory (3) Review of major properties of stochastic processes and Markovian-type queues. General theorems in the theory of queues; M/G/1 type systems; priority disciplines; conservative queues; Lindley's model; ordering and monotonicity; bounds and approximations; tandem queues; reversibility, symmetry, and networks; and applications. Avi-Itzhak. Prerequisite: 16:960:680.
16:711:557 (S) Dynamic Programming (3) Shortest path problems, label correcting algorithms, controlled Markov chains. Finite horizon control problems, discounted and undiscounted infinite horizon problems, average cost problems. Dynamic programming equations. Value and policy iterating methods, linear programming approaches. Applications in scheduling, inventory control, logistics, finance. Introduction to approximate dynamic programming. Ruszczynski. Prerequisites: Four semesters of calculus, linear algebra.
16:711:601,602 Seminar in Operations Research (0,0) Regular participation in the colloquia and seminars run by RUTCOR required of all M.S. and Ph.D. students.
16:711:611,612,613,614 Selected Topics in Operations Research (BA,BA,BA,BA) Topics of current interest relevant to operations research. Prerequisite: Permission of instructor.
16:711:631 (S) Financial Mathematics II (3) Options, futures and other derivatives, arbitrage pricing, Black-Scholes theory, exotic options, interest-rate models, stochastic programming models, and their applications to financial planning. Prekopa. Prerequisites: 16:198:521, 01:960:381.
16:711:695,696,697,698,699 Independent Study in Operations Research (BA,BA,BA,BA,BA)
16:711:701,702 Research in Operations Research (BA,BA)

See also courses listed under computer science, economics, industrial and systems engineering, statistics, and mathematics (applied mathematics), and in the doctoral program in management at the Graduate School–Newark, including the following courses:

16:198:510  Numerical Analysis (3)

16:198:513,514  Design and Analysis of Data Structures and Algorithms I,II (3,3)

16:198:521  Linear Programming (3)

16:198:522  Network and Combinatorial Optimization Algorithms (3)

16:198:524  Nonlinear Programming Algorithms (3)

16:198:526  Advanced Numerical Analysis (3)

16:198:528  Parallel Numerical Computing (3)

16:198:535  Pattern Recognition Theory and Applications (3)

16:198:538  Complexity of Computation (3)

16:198:541  Database Systems (3)

16:220:500  Mathematical Methods for Microeconomics (3)

16:220:501,502  Microeconomic Theory I,II (3,3)

16:220:503  Mathematical Methods for Macroeconomics (3)

16:220:507,508  Econometrics I,II (3,3)

16:220:545  Uncertainty and Imperfect Information (3)

16:220:546  Topics in Game Theory (3)

16:540:510  Deterministic Models in Industrial Engineering (3)

16:540:515  Stochastic Models in Industrial Engineering (3)

16:540:520  Supply Chain and Logistics Engineering (3)

16:540:530  Forecasting and Time Series Analysis (3)

16:540:555  Simulation of Production Systems (3)

16:540:560  Production Analysis (3)

16:540:565  Facilities Planning and Design (3)

16:540:568  Automation and Computer-Integrated Manufacturing (3)

16:540:585  System Reliability Engineering (3)

16:540:655  Performance Analysis of Manufacturing Systems (3)

16:540:660  Inventory Control (3)

16:540:665  Theory of Scheduling (3)

16:642:573,574  Numerical Analysis (3,3)

16:642:577,578  Selected Mathematical Topics in System Theory (3,3)

16:642:581  Graph Theory (3)

16:642:582,583  Combinatorics I,II (3,3)

16:642:585  Mathematical Models of Social and Policy Problems (3)

16:642:586  Theory of Measurement (3)

16:642:587  Selected Topics in Discrete Mathematics (3)

16:642:588  Introduction to Mathematical Techniques in Operations Research (3)

16:642:589  Topics in Mathematical Techniques in Operations Research (3)

16:960:540,541  Statistical Quality Control I,II (3,3)

16:960:542  Life Data Analysis (3)

16:960:563  Regression Analysis (3)

16:960:567  Applied Multivariate Analysis (3)

16:960:586,587  Interpretation of Data I,II (3,3)

16:960:590  Design of Experiments (3)

16:960:591  Advanced Design of Experiments (3)

16:960:593  Theory of Statistics (3)

16:960:652,653  Advanced Theory of Statistics I,II (3,3)

16:960:654  Stochastic Processes (3)

16:960:663  Regression Theory (3)

16:960:680,681  Advanced Probability Theory I,II (3,3)

16:960:689  Sequential Methods (3)

26:390:571  Survey of Financial Theory (3)

26:390:662  Investment Analysis and Portfolio Theory (3)

26:711:561  Introduction to Mathematical Economics (3)

26:711:652  Nonlinear Programming (3)

26:799:600  Supply Chain Modeling and Algorithms (3)

26:799:661  Stochastic Models for Supply Chain Management (3)

26:960:580  Stochastic Processes (3)

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