Models in Insurance and Finance I 
Actuarial Mathematics 16:711:531, Index # 12947
Instructor: Andras Prekopa
Topics: The economics of insurance. Individual risk
models. Survival distributions and life tables. Life
insurance. Life annuities. Net premiums. Multiple life
functions. Multiple decrement models. Collective risk models
for a single period. Collective risk models over an extended
period. Applications of ristheory. Insurance models including
expenses. Advanced multiple life theory. Population theory.
Theory of pension funding.
Text: Bowers, Gerber, Hickman, Jones, Nesbitt,
Actuarial Mathematics, second edition. The Society of
Acturaries, Ithaca, Ill., 1997. ISBN: 0938959468
Grading: Based on the solutions of homework problems
and a term project.
Case Studies in Applied
Operations Research Undergraduate: 01711481, Index
#45051 Graduate:
16:711:548, Index #49103
Instructor:
Sylvia Halasz, Office 148, RUTCOR
Building
sylviah@rci.rutgers.edu
Place
& Time:
RUTCOR Building, Room
139
M &
TH 6:30PM 
8:00PM
Prerequisites: Linear programming,
probability theory, statistics.
Objective:
Introduce the students to modeling reallife problems
and solving these using methods of operations research in its
broadest sense.
The necessary theory will be
reviewed.
In the
first half of the semester students will work on case studies
from the literature and present these in class. Parallel to this
everybody will look for a reallife problem where OR methods
can be used in the solution. In the second half of
the semester students will work on reallife projects and
present their results in class.
You can
start thinking of a project already now: a reallife problem
that you would like to solve – if not completely, at least
partially.
Examples:

timing of traffic lights on your way to
Rutgers

improve
public transport in a given area

how to
allocate the money in public
health

improve
the performance of an Internet search
engine
Grades
will be based on the solutions of the case studies (some of
which will be assigned as homework) and on the project
results.
Computational
Projects in Operations Research 16:711:517, 3 credits
Instructor: Time: Place:
RUTCOR Building, Room 139
Course Outline: The course will be highly
interactive with individual and group assignments and with
intensive computer practice. The students will be offered
various problems and projects to work on during the semester.
Some of the projects will involve the use of certain software
packages, while some others will require coding. In addition,
each of the students will be required to solve homework
assignments, mostly programming tasks. Grading will be based
on homeworks and projects.
The course concentrates on OR modeling and problem solving
with AMPL, a mathematical modeling language. Additionally,
elements of other programming environments will be described,
and a few assignments will be given, in particular, in PERL to
realize basic data structures and combinatorial algorithms; in
C++ to develop basic routines, and interface with CPLEX; and
in HTML, Javascript and CSS to develop home pages and
interactive webprojects.
Some related books:
 Robert Fourer, David M. Gay, and Brian W. Kernighan,
AMPL: A Modeling Language for Mathematical
Programming, (Duxbury Press/Brooks/Cole Publishing
Company, 1993).
 Daniel Gilly and the staff of O'Reilly & Associates,
Inc., UNIX in a nutshell, (O'Reilly & Associates,
Inc., Sebastopol, CA, 1992)
 D.E. Knuth, The Art of Computer Programming:
Fundamental Algorithms, (Addison Wesley, Reading, MA,
1973)
 Matematika, User's Manual, (Wolfram Research, Inc.,
1990)
 Chuck Musciano and Bill Kennedy, HTML  The
Definitive Guide, (O'Reilly & Associates, Inc.,
Sebastopol, CA, 1997)
 H. Schildt, C  The Pocket Reference, (Osborne
McGrawHill, Berkeley, 1989)
 Bjarne Stroustrup, C++ Programming Language,
(AddisonWesley, Reading, MA, 1997)
 Larry Wall, Tom Christiansen and Randal L. Schwartz,
Programming Perl, (O'Reilly & Associates, Inc.,
Sebastopol, CA, 1996)
Boolean Functions 16:711:553,
3 Credits
Instructor:
The course will describe the uses, the theory and the
algorithmic aspects of Boolean and of pseudoBoolean
functions, using frequently occurring models from operations
research, electrical engineering, and modern applied
mathematics. Among the important problems to be studied, we
mention the Satisfiability problem, dualization, determination
of prime implicants of Boolean functions, logic minimization,
quadratic 01 optimization, roofduality, MAXSAT, etc.
Important classes of Boolean functions (monotonic, regular,
Horn, threshold, etc.) and of pseudoBoolean functions
(supermodular, linearly separable) will be examined.
Numerous applications will be presented to computer
engineering, discrete optimization, artificial intelligence,
voting, game and reliability theory, etc.
Strong connections between linear programming, graph
theory, Boolean and pseudoBoolean functions, in the
development of algorithms for solving operations research
problems will be emphasized.
Prerequisites: Familiarity with graph theory and
linear programming is useful, but not absolutely
necessary.
Discrete
Optimiziation 16:711:513, 3 Credits
Instructor: Time: Place:
RUTCOR Building, Room 139 Prerequisites: Calculus,
Linear Algebra, Linear Programming
Background: Review of linear programming, the
ellipsoid algorithm. Introduction of graphs, networks, Boolean
and pseudoBoolean functions, polyhedral theory and integer
lattices. Elements of complexity theory.
Models: Knapsack, setcovering, (vehicle routing,
airline crew scheduling), packing, partitioning, clustering,
(stability number, voting districts, cuttingstock),
binpacking, scheduling, (jobshop, flowshop, onemachine),
plant location, transportation problems.
General and 01 Integer Programming: Formulations, LP
relaxation, rounding, unimodularity. Implicit enumeration and
branchandbound tecniques. Polyhedral description: vertices,
feasibility, valid inequalities, faces and facets. Value
function, surrogate, subadditive and Lagrangean duality.
Cutting planes, Gomory's algorithm, Chvatal cuts,
LovaszSchrijver cutting planes. Decomposition methods.
Preprocessing techniques and heuristics.
Graphs & Networks: Minimum paths, spanning
trees, max flowmin cut, CPM networks, matching algorithms.
Traveling salesman, Chinese postman.
Matroids, Submodular Optimization:Matroids, polymatroids,
"greedy" algorithms, submodular functions.
References:
 G.L. Nemhauser and L.A. Wolsey, Integer and
Combinatorial Optimization, J. Wiley, 1988.
 A. Schrijver, Theory of Linear and Integer programming,
J. Wiley, 1987.
 T. Lengauer, Combinatorial Optimization in Circuit
Layout Design, J. Wiley, 1990.
 C.H. Papadimitriu and K. Stieglitz, Combinatorial
Optimization: Algorithms and Complexity,PrenticeHall, 1982.
 L.A. Wolsey, Integer Programming, J. Wiley, 1998.
 W.F. Cook, W.H. Cunningham, W.R. Pulleyblank and A.
Schrijver, Combinatorial Optimization, J. Wiley, 1998
Pseudo Boolean
Functions 16:711:611, 3 Credits
Instructors: Time: Place:
Course Outline:
 Introduction, definitions and notations.
 Examples.
 General PseudoBoolean Functions  Representations of
pseudoBoolean functions, rounding procedures and
derandomization, persistency, local optima, basic algorithm,
reductions to quadratic optimization, posiform maximization,
l_{2}approximations and applications to game
theory.
 Quadratic PseudoBoolean Functions  Roof duality
(majoriztion, linearization, complementation, equivalence of
formulations and persistency, network flow model), hierarchy
of bounds (cones of positive quadratic pseudoBoolean
functions, complementation, majorization, linearization),
polyhedra, heuristics.
 Special classes  Sub and supermodular functions,
halfproducts, hyperbolic pseudoBoolean functions, products
of linear functions
 Approximation algorithms  MAXSAT and variants,
approximation of MAX2SAT via roofduality, approximation
of MAXSAT via convex majorization.
Financial
Mathematics 16:711:631:01, Index #54009
Instructor: Andras Prekopa Time: M.Th,
10:2011:40 AM Place: RUTCOR Bldg., Room
166 Prerequisites: Probability Theory, Linear
Programming.
Topics: Cash flow streams. Financial instruments
(stocks, bonds, futures, options, cash flows). Utility
functions. Arbitrage pricing theory. Application of
Martingales. Brownian motions. Ito's lemma. BlackScholes
theory. Parabolic PDEs and their numerical solutions. The
FeynmanKac solution. Exotic and pathdependent options
(chooser, barrier, lookback, Asian, Bermudan, etc.). Interest
rate models (Vasicek, HullWhite). Short introduction to
stochastic programming models.Markowitzďż˝s meanvariance
models. Bond portfolio composition models. Term
structures. The use of goal programming. Dynamic option
selection models. Value at Risk models.
Books: Below is a list of books which are useful to
study the subject. However, only parts of them will be used in
the course. A complete manuscript of the presentations will be
available.
 D. Duffie, Dynamic Asset Pricing Theory, Second Edition,
Princeton University Press, 1996.
 A. Prekopa, Stochastic Programming, Kluwer, 1995.
 P. Wilmott, S. Howison and J. Dewynne, The Mathematics
of Financial Derivatives. Cambridge University Press, 1997.
Grading: Based on the homework problem solutions and
the quality of a term project prepared by each student.
Office Hours: After class or by appointment.
Integer
Programming 16:711:465, Index #65540, 3
credits (Required course for the MINOR in Operations
Research)
Instructor: David Papp
(dpapp@eden,.rutgers.edu) Place: RUTCOR Building,
Room 139 Time: Tu & Fri, 10:2011:40 AM
Prerequisites: Calculus, Linear Algebra and Linear
Programming
Syllabus:ml:namespace
prefix = o ns = "urn:schemasmicrosoftcom:office:office"
/>
·
Modelling with integer
variables.
·
Specially structured problems: knapsack, covering and
partitioning problems.
·
An introduction to complexity theory: problems,
instances, worstcase complexity, polynomial algorithms, the
classes P and NP, polynomial reductions and
NPhardness.
·
Linear programming relaxations, integrality of
solutions, unimodularity and applications for assignment
problems, shortest path and network
computations.
·
Enumerative methods: branchandbound, implicit
enumeration, bounding techniques. Lagrangean and surrogate
duality.
·
Cutting planes, Gomory’s algorithm, lifting and
projecting for binary
optimization.
·
Heuristics: greedy algorithms, local search, truncated
exponential schemes.
Approved
Book: Integer
Programming, Laurence A. Wolsey
A
WileyInterscience Publication, John Wiley & Sons,
Inc. 1998
Handouts
will be provided.
Grading: Homework (20%),
Midterm (30%), and Final exam
(50%).
Introductory Topics in
OR 16:711:295,
Instructor: Office: Phone:
Email:
Text: Operations Research,
Applications and Algorithms (3^{rd} edition), Wayne L.
Winston, Duxbury Press
Course description: This course is an introduction
to the basic methods and models of Operations Research
(abbreviated O.R.): linear programming, network
models, integer programming, nonlinear programming, inventory
control, dynamic programming
O.R. can be described as follows (see text, p. 1) : "...
the term operations research (or, often, management
science) means a scientific approach to decision making,
which seeks to determine how to design and operate a system,
usually under conditions requiring the allocation of scarce
resources."
The course is computer based, using MS
Excel, and Solver (an addin to
Excel).
The study of the methodology of O.R. requires a working
knowledge of linear algebra and probability, and a good
understanding of calculus. These are expected of the students.
Grading Policy: There will be 810 homework
assignments (lowest grade discarded). Late homework will not
be accepted. The final grade will be assigned based on 20%
midterm, 40% homework, 40% final exam.
Nonlinear
Programming 16:711:612, 3
Credits Instructor: Office: Office
Hrs: Time: Place: Text:
Linear and Nonlinear Programming, S. G. Nash and A. Sofer,
McGrawHill, 1996
Syllabus:
 Unconstrained optimization:ďż˝ Optimality conditions,
Newtonďż˝s method, Line search and trust region methods,
 Methods for unconstrained optimization: Steepest
descent, QuasiNewton methods, Linear conjugate gradient
methods and truncated Newton methods, Nonlinear conjugate
gradient methods, Limitedstorage quasiNewton methods,
Nonlinear least squares methods,
 Constrained nonlinear optimization ďż˝ theory: Lagrange
multipliers and optimality conditions, Duality theory,
 Methods for nonlinear optimization: Reduced gradient
methods, Sequential quadratic programming methods, Exact and
inexact penalty methods and augmented Lagrangian methods,
 Barrier Methods: Classical interior point methods,
Infeasible interior point methods and merit functions, Line
search and trust region methods, Advanced topics Filters and
complementarity constraints.
Queueing
Theory 16:711:556
Instructor: Benjamin Aviâ€‘Itzhak
Topic Outline:
 Elements of Stochastic Processes: Definition of a
stochastic process; strict and covariance stationarity;
ergodicity; discrete time Markov chains; semiâ€‘Markov
processes and chains; embedded Markov chains; continuous
time Markov chains; birthâ€‘andâ€‘death processes; Poisson
processes; diffusion processes; Markovian queueing processes
and Jackson type networks.
 Definition of a queueing system; Little's theorem;
DAASSP (departures and arrivals see same picture) theorem;
the random observer; ROSTA (random observer sees time
averages), PASTA and ASTA theorems; the work in the system;
the random modification (remaining work in service); work
conserving schemes (disciplines) and the work conservation
theorem.
 Applications: the relation between queueing time and
queue size in M/G/1 type queues; busy period characteristics
in conservative M/G/1 type queues; nonâ€‘preemptive
priorities; optimal priority schemes; SRPF schemes.
 Generalized M/G/1 queues:The generic model; M/G/1; a
sequence of two servers in tandem with no intermediate
queue; server's breakdowns and vacations; preemptive repeat
and resume priorities; Takacs integroâ€‘differential
equation approach. A busy period approach; Gated queues with
limited batch sizes, unlimited batch sizes, processor
sharing, FIFO, LIFO and random selection for service.
 Lindley's GI/G/1 model; the Wienerâ€‘Hopf type integral
equation and its solution; bounds on the expected
equilibrium waiting time; Kingmans's heavy traffic
approximation; GI/M/1 example; Kendal's and Smith's theorems
for the conditional equilibrium distributions of waiting
times and lines in GI/M/r queues.
 Comparison methods for queues: Stochastic ordering;
convex and concave ordering; classes of distribution
functions (IFR/DFR, etc.); montonicity and comparability of
stochastic processes; monotonicity properties and bounds and
approximations for queueing processes.
 Tandem queues: Aviâ€‘Itzhak's theorem for deterministic
service times; bounding and approximations; optimal servers
ordering; justâ€‘inâ€‘time systems and throughput
approximations; strategies for deployment of flexible
servers; schemes for forkâ€‘join (split and match) systems;
correlated service times.
 Networks:Reversibility, quasiâ€‘reversibility, symmetric
queues and product form (kelly type) networks;
nonproductâ€‘form networks; approximations and bounds;
decomposition and aggregation methods, numerical methods.
 Applications of queueing models:Service systems; traffic
and transportation; computer systems; voice and data
communications; production and logistics. * It is not
possible to cover all the listed topics in depth in a one
semester course. Some of the topics will only be surveyed.
Prerequisites: Probability and elementary knowledge
of Stochastic Processes or Stochastic Models.
Grading: Home assignments, class presentations and
midterm(s) (take home) â€‘ 50 points, Final exam (possibly
take home) â€‘ 50 points
Reading: Home assignments include reading of a
number of journal publications in addition to specific
sections in the reference books.
Reference Books:
 L. Kleinrock, Queueing Systems, Vol. 1: Theory, Wiley
& Sons, 1975. (* Major reference book.)
 L. Kleinrock, Queueing Systems, Vol. 2: Computer
Applications, Wiley & Sons, 1976.
 J.W. Cohen, The Single Server Queue, Northâ€‘Holland,
1982.
 F.P. Kelly, Reversibility and Stochastic Networks, Wiley
& Sons, 1979.
 D.R. Cox and W.L. Smith, Queues, Wiley & Sons, 1961.
 L. Takacs, Introduction to the Theory of Queues, Oxford
University Press, 1962.
 D. Stoyan, Comparison Methods for Queues and Other
Stochastic Models, Wiley & Sons, 1985.
 J. Walrand, An Introduction to Queueing Networks,
Prentice Hall, 1988.
 A.E. Conway and N.D. Georganas, Queueing
Networksâ€‘Exact Computational Algorithms, MIT Press, 1989.
 R.W. Conway, W. L. Maxwell and L.W. Miller, Theory of
Scheduling, Addisonâ€‘Wesley, 1967.
 D. Gross and C.M. Harris, Fundamentals of Queueing
Theory, Wiley & Sons, 1974.
 D.P. Heyman and M.J. Sobel, Stochastic Models in
Operations Research (two volumes). McGrawâ€‘Hill, 1982.
 J. Riordan, Stochastic Service Systems, Wiley &
Sons, 1962.
 R.W. Wolf, Stochastic Modeling and the Theory of Queues,
Prentice Hall, 1989.
Game Theory 16:711:613,
Index #07284, 3 credits
Instructor: Vladimir Gurvich
(gurvich@rutcor.rutgers.edu)
RUTCOR, Room 117,
7324453235 Location:
RUTCOR Building, Room 139 Time:
T, 1:404:40 PM Place:
RUTCOR Building, Room 139
Course
Outline:
<![if
!supportLists]>
1.
<![endif]>Matrix games, max min , min max and
saddle point. Pure and mixed
strategies. Solvability in mixed
strategies. Von Neumann's Theorem for
matrix games.
<![if
!supportLists]>
2.
<![endif]>Bimatrix and nmatrix
games. Nash equilibria and Nash
solvability. Perfect equilibria and perfect
solvability. Sophisticated equilibria and
dominance solvability.
<![if
!supportLists]>
3.
<![endif]>Games in extensive, positional and
normal form. Perfect information and
solvability in pure strategies. Nash
solvability of the cyclic games.
<![if
!supportLists]>
4.
<![endif]>Domination and dominance solvability.
Backward induction. Dominance solvable
extensive and secret veto voting schemes.
<![if
!supportLists]>
5.
<![endif]>Cooperative games.
Coalitions. Transferable and
nontransferable utilities, TU and NTUgames.
Cores and coresolvability.
BondarevaShapley's Theorem and Scarf's Theorem.
<![if
!supportLists]>
6.
<![endif]>Effectivity functions and game forms,
MoulinPeleg's Theorem. Cooperative games
in effectivity function form, Keiding's Theorem.
Stable effectivity functions and stable families of
coalitions.
<![if
!supportLists]>
7.
<![endif]>Intrduction to Social Choice Theory.
Paradox Arrow. Social choice functions and
correspondences.
<![if
!supportLists]>
8.
<![endif]>Boolean functions and graphs in game
theory:
Boolean duality and Nash solvability.
Readonce Boolean functions, P4free graphs and normal
form of the
positional games with
perfect information. Stable effectivity
functions and Berge's perfect graphs.
Stable families
of coalitions and normal hypergraphs. The
Shapley value and the Banzhaf power index for cooperative
games and approximation
of pseudoBoolean functions.
No
Prerequisites, graph theory and linear programming would be
useful but not necessary.
Simulation 16:711:613, 3
Credits Instructor: Phone:
Email: Website: Time:
Place: Text: Simulation with Arena
(2^{nd} edition), W. David Kelton, Randall P.
Sadowski, Deborah A. Sadowski, McGrawHill 2002
Detailed Outline:
1 
Introduction to discrete event
simulation 
1, 2 
2 
Random number generation, Intro. To
ARENA 
4, 5.15.3 
3 
ARENA basics 
5.45.8 
4 
Model testing and debugging 
6 
5 
Input analysis 
7 
6 
Model verification and validation 
8 
7 
Output analysis 
9 
8 
Advanced ARENA modelingproduction models
1 
11 
9 
Advanced ARENA modelingproduction models
2 
11 
10 
Advanced ARENA modelingtransportation
models 1 
12 
11 
Advanced ARENA modelingtransportation
models 2 
12 
12 
Advanced ARENA modelinginformation
systems 1 
13 
13 
Advanced ARENA modelinginformation
systems 2 
13 
14 
Advanced ARENA modelingother
topics 
Semidefinite and Second Order
cone Programming 16:711:613
Instructor:
Semidefinite programming (SDP) is a relatively new topic in
optimization theory that emerged in early nineties. It has
attracted considerable attention for several reasons. First it
is a natural model that pops up in diverse application areas
from combinatorial optimization and graph theory, to
statistics, to many areas of engineering. Second the
underlying problem is now fairly wellunderstood and it is
possible to come up with both theoretically and pragmatically
efficient algorithms. Third, the subject has intellectual
appeal in that methods from several areas of mathematics come
together to form an elegant theory.
In this course we present a rather comprehensive survey of
the subject. We will overview semidefinite programming, study
duality and complementarity conditions, and cover at least one
class of interior point algorithms. We will survey several
areas of applications. For instance in combinatorial
optimization we study Lovasz theta function and
GoemansWilliamson approximation algorithm to the MAXCUT and
related problems. We will study one or two applications in
statistics and finance. For instance we study the connection
to Markowitz portfolio selection theory and to statistical
optimal experiment design. We will also study the connection
to positive polynomials and moment problems and theory
implications in shape constrained approximation and
regression. Our coverage will be mathematically deep, though
almost all preliminary material will be reviewed. In
particular we shall cover the theory of Euclidean Jordan
algebras and their relevance to the most elegant formulation
of SDP and its generalization.
Prerequisites: Ph.D. standing and the proverbial
"mathematical maturity" are the only prerequisites. Knowledge
of linear programming will be quite helpful though strictly
speaking not required. Good understanding of linear algebra is
essential.
Student Requirements: Each student is required to
take turn and jot down notes during the lectures and then
transcribe them into LaTeX. The notes will then be posted in
the course web page. In addition each student is required to
prepare a 3040 minute talk which can be either presentation
of a research paper by others or it can be a project that
he/she has conducted in the course.
Reading: There is no official textbook. Relevant
papers will be made available in the course home page.
Stochastic Models in
Operations Research 01:640:424, 3 Credits
Instructor: Time: Place:
RUTCOR Building, Room 166 Office Hourse: M, Th,
after class or by arrangement
Topics: Markov chains: definition, transition
probabilities, special Markov chains (random walks, dams and
inventories, branching processes), classification of states,
limit theorems. Poisson processes: derivations, homogeneous,
nonhomogeneous processes, spacial and marked Poisson
processes. Continuous time Markov chains: the
ChapmanKolmogorev equation, birth and death processes, the
case of a finite state space, special cases, limiting
behavior. Renewal processes: definition, the renewal function,
replacement models, renewal theorems, inspection paradox,
applications. Brownian motions: definition, processes with
independent increments, the maximum variable and the
reflection principle, Brownian bridge, geometric Brownian
motion, applications in modern financial theory. Queueing
theory: queueing systems, Little's formula, Poisson arrivals
and exponential and general service times, the case of an
infinite number of servers, priority queues, queueing
systems.
Prerequisites: Probability Theory
Book: H. M. Taylor and S. Karlin, An Introduction to
Stochastic Modeling, 3^{rd} edition, Academic Press,
1998. ISBN: 0126848874.
Grading: based on the homework problem solutions and
the results of two exams; one midterm and one final.
Stochastic Models in
Operations Research 16:711:525, Index
#48234 Instructor: Benjamin AviItzhak, RUTCOR
Bldg., Room
125
Aviitzha@rutcor.rutgers.edu
7324453183
Time: Tu, 1:40  4:40
PM Place: RUTCOR Building, RToom
139 Office hours: Prerequisites:
Probability Theory (640:477 or equivalent)
Topics:
 Review of basics in the axiomatic theory of probability.
 Definition of a stochastic process. Classification of
stochastic processes.
 Discrete time Markov Chains. Transition probabilities.
Classification of states. Limit theorems. Applications.
Markov decision processes. Applications.
 Poisson processes.Derivations of the process from
postulates. Properties of the exponential distribution.
Planar and special random point distributions. Applications.
 Continuous time Markov chains. Kohmogorov equations.
Birth and death processes. Stationary distributions.
Applications.
 Renewal theory. Elementary renewal theorem. Renewal
equation. Renewalreward processes.
 Brownian motion process. Refection principle and
distribution of a maximum. Valuation of financial
derivatives.
 Queueing systems. Basic notions. The M/M/s system with
finite and infinite capacities. Elements of queueing
networks.
Book: Sheldon M. Ross, "Applied Probability
Models with Optimization
Applications"
Dover Publications, soft cover, 1992. ISBN:
0486673146
Grading: Based on the solutions of the homework
problems and the results of the written midterm and final
exams.
Office hours: after class or by appointment.
Stochastic
Programming 16:711:555, Index #14290, 3 Credits
Instructor: Andras Prekopa Time: M,F
10:2011:40 AM Place: RUTCOR Bldg., Room 139
Stochastic programming is a rapidly developing area. It is
on the border line of statistics and probability theory on the
one hand and mathematical programming on the other hand. It
can be defined as a methodology to optimize the design and
operation of stochastic systems by the use of mathematical
programming tools.
Topics: Overview of statistical decision
principles.Overview of stochastic programming model
constructions: reliability type models, penalty type models,
mixed models, static and dynamic type models. The simple
recourse model and its numerical solution techniques.
Convexity theory of probabilistic constrained models.Bounding
and approximation of probabilities. Numerical solution of
probabilistic constrained models. Twostage programming under
uncertainty and the solution of the relevant problem by
Benders' decomposition. Multistage stochastic programming
models. Scenario aggregation. Distribution theory of
stochastic programming. Applications to production, inventory
control, water resources, finance, power and communication
systems.
Prerequisites: Probability theory, linear
programming
Book: A. Prekopa, Stochastic Programming, Academic
Publishers 1995. (The instructor will make available a few
printed copies for the audience.)
Grading: Based on the solutions of the homework
problems and the quality of a term project work. Each student
will have his/her own coursework subject following an
agreement with the instructor.
Theory of Linear
Optimization 01:711:453, Index #05425, 3
credits 01:640:453, Index #05486, 3
credits Master students must register under 16:711:614 for
credit toward their MS degree.
Instructor: David Papp Time: Tu, Th,
5:006:20 PM Place: RUTCOR Building, Room
166 Office Hours:
BA, or after class. Room 143, RUTCOR Bldg.
Topics include convex sets, polyhedra, Farkas lemma,
canonical forms, simplex algorithm, duality theory, revised
simplex method, primaldual methods, complementary slackness
theorem, maximal flows, transportation problems, 2person game
theory.
Prerequisite: 01:640:250 Introductory Linear
Algebra
Book to be used: Linear Programming, Vasek Chvatal,
W. H. Freeman and Company 1980. Available at the Bookstore on
College Avenue.
Partition:
Optimality and Clustering 16:711:612, Index #45737
Instructor:
Uriel Rothblum, rothblum@ie.technion.ac.il Room 102,
RUTCOR
Building
Place
& Time:
RUTCOR Building, Room 139 or
166
Monday –
1:404:40PM
Syllabus:
Partition
problems constitute a large class of combinatorial
optimization problems.
Of particular interest are problems where it is
possible to restrict attention to solutions that exhibit
clustering properties.
Several venues that accomplish this goal will be
presented.
Specific topics that will be covered.
1. Classification of
multiparameter partition
problems
2. Applications
3. Optimality of vertices
and enumeration of vertices
4. Geometric clustering
properties of partitions (discussing polynomial
enumerations)
5. Partition problems with
optimal partition that exhibit clustering
properties
6. Consistency and
sortability of partition
properties
7. Single
parameter partition
problems
The
course will be using a draft of a book and chapters will be
distributed to students.
Convex Analysis and
Optimization 16:711:611, Index
#45261
Instructor:
Jonathan Eckstein
Time:
Wednesday, 1:40PM – 4:40PM
Place:
RUTCOR Bldg., Room 166 or 139
Prerequisites: "Basic knowledge of
finitedimensional real analysis: open
sets, closed sets, and convergence of
sequences."
Topics:
Fundamentals of
finitedimensional convex sets and functions. Subgradient
mappings, optimality conditions, and Lagrange multipliers.
Setvalued monotone operators, conjugate functions, and
optimization duality theory. Convexanalytic
optimization algorithms such as subgradient, proximal, and
bundle methods, including applications to
nonconvex/discrete optimization.
Book: "Convex Analysis
and Optimization", by Bertsekas, Nedic, and Ozdaglar,
details at http://www.athenasc.com/convexity.html.
Grading: Grades will be based
on two takehome exams and homework assignments
given out every one or two weeks.
Office Hours: Tuesdays 2:003:30PM
and by appointment.
Advanced
Mathematical Topics 16:711:611, Index
# 02005, 3 credits
Instructor:
Time:
Location:
Room 139,
RUTCOR
Building Office
Hours: After class or by
arrangement
Course
Outline: The course consists of a range of
topics, with original material, drawn from the instructorâ€™s
experience in industry. A review of partial
fractions and the properties of the derivative D operator are
given with applications to the solution of differential
equations and Volterra integral equations.
Application is made to queues with
reneging. Eulerâ€™s summation method is
given with applications to determining expectations of
functions of random variables. The
Newton expansion and its applications to
interpolation and summation of series are studied including
the determination of maxima of orbits and tides.
Applications of the Laplace transform are introduced.
The summation of theory of Norlund which permits a
modern, unified way of solving linear difference equations
with continuous argument and especially with variable
coefficients, obtaining asymptotics, and summing series is
extensively studied.
A sample of related books to
follow......
Back to RUTCOR
page. 