I am requesting that I be considered for promotion to full professor in the Department of Operations Research and Engineering (ORE) in the School of Information Technology and Engineering (IT&E) at George Mason University (GMU). This personal statement summarizes my professional accomplishments, with a particular emphasis on my accomplishments since joining GMU in 1987. I think that this summary demonstrates clearly that I am a productive faculty member, that I have made significant contributions to my department, university, and research field, and gives a strong indication that I will continue to be productive and effective in the years ahead.

Here is an outline of my personal statement: Section 1 contains background information, Section 2 discusses my teaching, Section 3 gives an overview of my research interests and activities, Section 4 describes plans for future research. Section 5 summarizes my publication record, Section 6 discusses sponsored research, Section 7 describes my professional service record, and Section 8 contains concluding remarks.

I am currently an associate professor in the Operations Research and Engineering Department at George Mason University. I joined the university as an untenured associate professor in 1987, and was granted tenure in 1990. Prior to that I was an Assistant Professor in the Mathematical Sciences Department at The Johns Hopkins University.

I graduated in June 1982 from Stanford University, with a Ph.D. in Computer Science. My thesis, titled "Truncated Newton Methods," was supervised by Walter Murray of the Operations Research Department. I obtained my B.Sc. (Honors) degree in Mathematics from the University of Alberta (Edmonton, Canada) in May 1977.

In addition to my position at GMU, I also have a part-time position as a Computer Scientist at the National Institute of Standards and Technology in Gaithersburg, Maryland. During the summer of 1986, I was a Resident Associate at the Argonne National Laboratory in Argonne, Illinois. In spring 1995, I will be on Faculty Leave at Rice University in Houston, as a visitor to the Center for Research on Parallel Computation.

My research specialization is in the area of computational mathematics, and more specifically computational optimization. A number of my colleagues (Terry Friesz, Karla Hoffman, Roman Polyak, and Ariela Sofer) have related research interests, and so I see myself as contributing to one of the department's most important research and teaching activities.

I have taught courses at GMU at all levels from freshman to doctoral, and in addition have supervised doctoral students. I have also taught in several different divisions of the university, and have been involved in the development of new courses, as well as with more general curriculum reform.

Throughout this period I have been able to achieve consistently excellent teaching ratings, details of which are included in a table that is part of my vita. Some indication of these results can be obtained from the responses to the statement, "This course is taught well." My average score on this statement since joining GMU has been 4.55 (out of 5), and for the last four years my average score has been 4.83, with no score below 4.7.

In addition to the evaluations, a number of students have written letters or comments praising my teaching. Examples of these are included in my Teaching Portfolio.

Within the doctoral INFT program, I have taught INFT 881, Numerical Methods for Mathematical Optimization, as well as the introductory course INFT 500, Quantitative Foundations I (seven times).

Within the ORE department, I have taught many of the core courses in deterministic operations research. These include OR 641, Linear Programming, OR 644, Nonlinear Programming, OR 682, Computational Methods in Engineering and Statistics (five times), and OR 541, Operations Research I (seven times). The course OR 682 is one I developed. It is cross-listed with courses in STAT, MATH, and CSI, and so serves several graduate programs at GMU.

At the undergraduate level, I have taught several courses in the PAGE program. These were PAGE 120, Computers in Society (three times, twice as course organizer) and PAGE 125, Quantitative Analysis. In connection with PAGE 120, I was also a member of the PAGE Executive Committee from 1988 to 1990.

Another course that I developed, OR 481, Numerical Methods in Engineering, will be offered in spring 1995. It will be cross-listed with MATH 446, a course I am teaching currently.

I have served or am serving as the doctoral dissertation supervisor for four students. Paul Anderson graduated in June 1992. Hossein Fateh is expected to complete his degree work in January 1995. Two other students—Ted Carniol and Richard Shaffer—are in the process of their doctoral degrees within the CSI program.

I am currently chair of the IT&E Initiatives Committee, a committee that is examining reforms to the entire IT&E curriculum. This activity is discussed below in Section 6.

Teaching is an important part of my work. I work to keep my courses up to date, and experiment with new teaching techniques in order to become more effective in the classroom. For example, in my courses OR 682 and Math 446 this semester (fall 1994), I am implementing approaches proposed in the report of the IT&E Initiatives Committee, the curriculum reform committee that I chair. In addition, I am the co-author of two textbooks (see Section 4).

My research interests are in numerical analysis. The bulk of my research has been in the area of optimization, in particular the numerical solution of (usually large) nonlinear optimization problems. The work in the other areas has been more diverse, and is described in more detail below.

My optimization work has been concerned with the numerical solution of nonlinear optimization problems. (These are an important class of mathematical models arising in many areas of science and engineering, and involve the maximization or minimization of some objective function, perhaps subject to constraints on the variables.) Many of the papers focus on truncated-Newton methods, a class of numerical methods suitable for solving large optimization problems. This research began with my Ph.D. thesis. The software package that arose out of my thesis work (called TN/TNBC) has been widely used on problems having up to several hundred thousand variables. The software is part of the online Netlib collection. It is considered to be one of the most robust and efficient codes for large-scale unconstrained nonlinear optimization available. Its performance is documented and analyzed in my paper with J. Nocedal of Northwestern University.

A later series of papers (with A. Sofer of GMU) is concerned with numerical methods suitable for parallel computing. This work also led to the development of a software package (called BTN). This software is in the Netlib collection as well, and was published in the software journal ACM Transactions on Mathematical Software. This work is significant in several respects:

• it is the only publicly available software for large-scale parallel unconstrained optimization;
• the software runs on a variety of parallel computers, both shared- and distributed-memory;
• it is one of the few implementations of any complex numerical algorithm on a distributed-memory parallel computer;
• the software has been able to solve a wide variety of optimization problems effectively on a parallel computer, problems having up to 100,000 variables.

My most recent papers in this area (again with A. Sofer of GMU) focus on large constrained optimization problems. This work has shown that interior-point methods for constrained problems can be applied safely to nonlinear problems. (Interior-point methods have been tremendously successful at solving linear programming problems, but since 1970 had been considered computationally unstable in the nonlinear case.) The research has also shown that these interior-point methods can be applied to large problems, and that the algorithms and software that we have developed for the unconstrained case (including the parallel algorithms and software) can be adapted to this new context.

While on Faculty Leave at Rice University, I plan to continue work in this area, examining in greater detail parallel algorithms for large constrained nonlinear optimization problems, an area for which few results are available.

I also have done research in a number of other areas in computational mathematics. I have published several papers in the area of numerical linear algebra. Three of these papers (with R. Byers, G. Golub, and C. Van Loan) are concerned with problems arising in control theory. The paper with Golub and Van Loan, together with its accompanying software, remains the standard method for this particular problem.

I have also published papers in the area of computational statistics. Three of these papers (with G. Golub and V. Klonias) describe the solution of certain data fitting problems.

There are also some miscellaneous papers. These represent the solution of applied problems (in astrophysics and ecology), encyclopedia articles, guidelines for computational testing, historical studies, and reviews.

For the next few years (at least) I plan to continue my study of algorithms for large constrained nonlinear optimization problems, a problem area for which few successful techniques are available. There are several aspects to this plan of study, and these are outlined below.

This work will build upon my past research, work I have completed on parallel and scalar algorithms for large unconstrained problems, and the work on interior-point methods and preconditioners. These will be important building blocks for the development of sophisticated practical methods for constrained problems.

In spring 1995, I will be visiting the Center for Research on Parallel Computation at Rice University. This Center includes many prominent researchers in the areas of parallel computing and nonlinear optimization. I expect to use this time to research the application of our existing parallel algorithms to a wider and more difficult class of applied problems, as well as to develop new parallel algorithms for the constrained case.

I also plan to continue studying very difficult applied optimization problems, such as the x-ray crystallography problem that was the subject of the Ph.D. thesis of my advisee, Paul Anderson. In summer 1995, I have been invited to be a participant in a workshop on this topic at the Institute for Mathematics and its Applications at the University of Minnesota. This workshop will provide an opportunity to further study the solution of this problem.

Many researchers (including myself) believe that special-purpose algorithms will be required to solve the most difficult optimization problems, and so the study of particular applications is important to the advancement of research in nonlinear optimization. I anticipate that the x-ray crystallography application will be one of a number of applied problems that I study in the coming years.

There is one further major area of investigation that I expect to study. Many large optimization problems arise as the discretization of problems from optimal control. (The original problems are infinite dimensional, i.e., their solution is a function, and some finite-dimensional approximation to the solution is computed instead.) The standard algorithms for nonlinear optimization are not tailored to this situation, even though it represents a huge class of problems. I have begun initial research in this area in collaboration with Richard Shaffer, one of my Ph.D. advisees.

I am the co-author of two books, editor or co-editor of two others, and the translator of a fifth. I am author or co-author of 30 research papers, 7 other scientific papers (e.g., reviews), and 6 technical reports. I have translated 3 other scientific papers. The papers have appeared in a wide variety of journals, including the most prestigious journals in my field (for example, Mathematical Programming, various SIAM journals, and the Journal of the American Statistical Association).

The book

• David K. Kahaner, Cleve Moler, and S.G. Nash, Numerical Methods and Software, Prentice-Hall (1989)

is a textbook designed for upper-level undergraduate and low-level graduate courses. It is currently in its eighth printing, with well over 10,000 copies in print. In February 1989, it was an alternate selection for the Library of Information and Computer Science Book Club. The list of schools that have adopted this book as a text includes: The George Washington University, Georgia Institute of Technology, The Johns Hopkins University, Stanford University, State University of New York at Buffalo, University of California at Berkeley, University of Maryland at College Park, and Cornell University.

The book

• Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, McGraw-Hill, to appear (1995)

is also a textbook designed for upper-level undergraduate and low-level graduate courses. It is currently in its final stages of preparation, and will appear next year. Two other publishers offered us contracts for this project. The manuscript has been class-tested in several courses here at George Mason. It has also been used for two courses at the University of Iowa, and will be used in the spring at UCLA.Although this is a textbook, it contains a great deal of advanced materials, material that is important in our research, particularly on constrained optimization problems. We felt it was essential to the long-term success of our research to have a complete, broad, and thorough knowledge of linear and nonlinear programming, and the writing of this book was a way to accumulate, clarify, and solidify this knowledge. A great deal has changed in our field since 1984 (when interior-point methods for linear programming were first developed) and this book has given us a solid foundation in this new work.

The book will also (we expect) be of value to other researchers, since it contains a great deal of material that has never before appeared in book form. A number of theoretical results are included that were either scattered over several research papers, or that were incorrect in their published versions. Many other results are presented here with new (often simplified) proofs, so that a great deal of material is made available for the first time to a broad audience. We also have extensive and up-to-date discussions of interior-point methods as well as computational issues that are lacking in other textbooks. It is generally accepted that currently there is no good text in this area, and we are trying to fill that need.

The book

• Stephen G. Nash (editor), A History of Scientific Computing, Addison-Wesley (1990)

is a record of the conference of the same name that was held at Princeton University in 1987, and is part of a series of books being published by Addison-Wesley and the Association for Computing Machinery on the history of computing. It is not simply a collection of papers from the conference. I took an active role in editing the papers (sometimes extensively) and provided introductory and connective materials.

The book

• Stephen G. Nash and Ariela Sofer (editors), The Impact of Emerging Technologies ..., Kluwer Academic Publishers, to appear (1994)

is the proceedings of a conference of the same name organized by us in Williamsburg in January 1994. This is a refereed volume of papers from the conference.

Many of my publications have been co-authored. This is typical for my field, where (based on a survey of recent journal issues) about 75% of the papers have multiple authors. This is not surprising in research that requires a sophisticated interaction of mathematical theory, algorithmic expertise, and supercomputing experience. In fact, agencies such as the National Science Foundation are actively encouraging collaborative research, since it is seen as an essential element of up-to-date research in computational fields. It is becoming difficult to get funding without evidence of such collaborations.

But for two exceptions, all of my papers list the authors in alphabetical order. This corresponds to a balanced team effort on the part of the contributors. I consider this to be especially true of the work I have done with Ariela Sofer; this is an equal partnership. We both take an active role in doing research, supervising students, giving talks, attending meetings, writing papers, writing grant proposals, programming, and computational testing.

I have been supported by grants and contracts ever since receiving my Ph.D. For all of these grants, I was either Principal Investigator or co-Principal Investigator. The Initiation Grant from The Johns Hopkins University was a small ``get-started'' grant. The 1983 National Science Foundation (NSF) grant was a two-year research grant ($____). The 1984 NSF grant ($____) was an equipment grant, for computing equipment to support my other research grants. The 1985 Air Force grant ($____) was a three-year research contract. The 1989 Center for Innovative Technology grant ($____) was used for equipment and summer research support. The 1991 NSF grant ($____) was a three-year research grant. The 1994 NSF grant ($____) is also a three-year research grant.

I have an active service record. I have served on committees at various levels within the University. I am on several editorial boards. I have been a conference organizer. I have had research appointments at national laboratories. I have had official positions in professional societies. Some of these activities are described in more detail below.

For many years, I have been a regular, often weekly, visitor at the National Institute of Standards and Technology (formerly the National Bureau of Standards). I have a part-time appointment as a Computer Scientist. I act as a specialist in the area of computational optimization. In that capacity, I offer consulting advice to scientists at the facility, teach short courses, and do research. Several publications have results from this association (those with P. Boggs, D. Kahaner, and B. Rust, listed in my vita). This is a continuing position. The work with the Computational Testing Committee of the Mathematical Programming Society grew out of this position.

I have been an active participant in the SIAM Activity Group on Optimization, a special interest group within SIAM. I have served on the Advisory Board, as Secretary-Treasure, and as editor of the Newsletter. I am currently on the Board of Directors of ACM SIGNUM, a special interest group within the ACM.

I was a General Chair (with Ariela Sofer) of the ORSA/CSTS Conference in Williamsburg (January 1994). An associated conference proceedings will soon be published, edited by the two of us. I have also assisted with the organization of five other conferences; see my vita for details.

I am on the editorial boards of three journals. I have been an editor of the Journal of the American Statistical Association since 1990, and an editor of the SIAM Journal on Scientific Computing since 1991. I have been asked to be an Area Editor of the ACM Journal of Experimental Algorithmics (Series B), a new electronic journal that is expected to begin publication in 1995.

I have served on a number of review panels for granting agencies, and have reviewed grant proposals on many occasions. I review papers regularly for a wide variety of publications. I have also served as a reviewer for book projects at several publishing firms. Again, see my vita for details.

Within the University, I have served on many committees at the department, school, and university level. I am currently chair of the IT&E Initiatives Committee, a committee charged with examining curricular reform within the school of engineering. This committee prepared a major report in spring 1994, and also submitted a grant proposal to the National Science Foundation in summer 1994.

This statement (especially when combined with my vita and my teaching portfolio) provides a detailed summary of my career, particularly that portion of my career spent at George Mason University. I believe it demonstrates a record of commitment and accomplishment in all relevant areas.

In teaching I have developed new courses, written textbooks, achieved consistently excellent teaching ratings, supervised Ph.D. students, and been a member of a great many doctoral committees, as well as contributing to curricular reform within the university.

I have been an active researcher, publishing extensively, and achieving significant results especially in the area of nonlinear optimization. This research work has been repeatedly supported by research grants from major funding agencies.

I have been active within my profession, serving on boards and committees at professional societies, organizing conferences, and serving as an editor on journal editorial boards.

I have also been active within the university, serving on committees at all levels.

This commitment to the University and to my profession has been consistent and continuous since receiving my Ph.D. in 1982. There is every indication that it will continue into the future. Based on this record, I am requesting the faculty to recommend my promotion to full professor.