Richard Cottle
Professor of Management Science and Engineering, Emeritus
Bio
Richard W. (Dick) Cottle was born in Chicago in 1934. He received his elementary and high school education in the neighboring village of Oak Park. Dick enrolled at Harvard College to take up political science and premedical studies in order to become a physician (or possibly a foreign service officer if that didn't work out). As it happened, both of these alternatives were abandoned because he was strongly attracted to mathematics and ultimately received his bachelor's degree in that field. He stayed on at Harvard and received the master's degree in mathematics in 1958. This was the Sputnik era, and Dick was moved by a passion to teach secondarylevel mathematics. In the first of a series of fateful decisions, he joined the Mathematics Department at the Middlesex School in Concord, Massachusetts where for two years he taught grades 712. Midway through this period he married his wife Suzanne (Sue). At this time he began to think of returning to graduate school for a doctorate in mathematics. He decided to study geometry at the University of California at Berkeley and was admitted there. Just before leaving Middlesex, Dick received a telephone call from the Radiation Laboratory at Berkeley offering him the part time job as a computer programmer for which he had applied. Through this job, he became aware of linear and quadratic programming and the contributions of George Dantzig and Philip Wolfe. Before long, Dick left the Rad Lab to join Dantzig's team at the Operations Research Center at UC Berkeley. Under the tutelage of George Dantzig (and the late Edmund Eisenberg), Dick developed a symmetric duality theory and what was then called the "composite problem". These topics along with a reÃ«xamination of the Fritz John conditions, formed the core of his doctoral dissertation. The composite problem involved a fusion of the primal and dual firstorder optimality conditions. It was realized that the resulting inequality system could be studied without reference to the primaldual structure out of which it was born. The name "complementarity problem" was suggested by Dick and introduced in a joint paper with Habetler and Lemke. After Berkeley, Dick's work took two closely related directions. One was the study of quadratic programming; the other was what we now call "linear complementarity". The interesting role played by classes of matrices in both these areas has always held a special fascination for Dick. In quadratic programming, for instance, with Jacques Ferland he obtained characterizations of quasi and pseudoconvexity of quadratic functions. Dick (and others) were quick to recognize the importance of matrix classes in linear complementarity theory. It was he who proposed the name "copositiveplus" for a matrix class that arose in Lemke's seminal paper of 1965. The name first appeared in the classic paper of Cottle and Dantzig called "Complementary Pivot Theory of Mathematical Programming". The subjects of quadratic programming and linear complementarity (and the associated matrix theory) remain central to his research interests.
Academic Appointments

Emeritus Faculty, Acad Council, Management Science and Engineering
All Publications

On "Prehistoric" Linear Programming and the Figure of the Earth
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
2017; 175 (1): 255–77
View details for DOI 10.1007/s1095701711655
View details for Web of Science ID 000412163800013

Some LCPs solvable in strongly polynomial time with Lemke's algorithm
MATHEMATICAL PROGRAMMING
2016; 160 (12): 477493
View details for DOI 10.1007/s1010701609964
View details for Web of Science ID 000385191700017

A brief history of the International Symposia on Mathematical Programming
20th International Symposium of Mathematical Programming (ISMP)
SPRINGER. 2010: 207–33
View details for DOI 10.1007/s1010701004008
View details for Web of Science ID 000282829600002

A field guide to the matrix classes found in the literature of the linear complementarity problem
JOURNAL OF GLOBAL OPTIMIZATION
2010; 46 (4): 571580
View details for DOI 10.1007/s108980099441z
View details for Web of Science ID 000275457000010

Harry Markowitz and the Early History of Quadratic Programming
International Symposium on Forecasting
SPRINGER. 2010: 179–211
View details for DOI 10.1007/9780387774398_8
View details for Web of Science ID 000274754900008

New characterizations of row sufficient matrices
LINEAR ALGEBRA AND ITS APPLICATIONS
2009; 430 (1112): 29502960
View details for DOI 10.1016/j.laa.2009.01.010
View details for Web of Science ID 000266154700011

Closedform solution of a maximization problem
JOURNAL OF GLOBAL OPTIMIZATION
2008; 42 (4): 609617
View details for DOI 10.1007/s1089800893382
View details for Web of Science ID 000260377600010

Estimating ordered parameters by linear programming
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
2008; 138 (9): 26222633
View details for DOI 10.1016/j.jspi.2008.03.005
View details for Web of Science ID 000256602600005

Sufficient matrices belong to L
MATHEMATICAL PROGRAMMING
2006; 106 (2): 391401
View details for DOI 10.1007/s1010700506397
View details for Web of Science ID 000235062200009

Measuring conformability of probabilities
STATISTICS & PROBABILITY LETTERS
2001; 52 (3): 321327
View details for Web of Science ID 000168400900012

Quartic barriers
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
1999; 12 (13): 81105
View details for Web of Science ID 000080941900006

ON A SUBCLASS OF P0
LINEAR ALGEBRA AND ITS APPLICATIONS
1995; 224: 325335
View details for Web of Science ID A1995RF72200021

PSEUDOMONOTONE COMPLEMENTARITYPROBLEMS IN HILBERTSPACE
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
1992; 75 (2): 281295
View details for Web of Science ID A1992KB23000003

LEASTINDEX RESOLUTION OF DEGENERACY IN LINEAR COMPLEMENTARITYPROBLEMS WITH SUFFICIENT MATRICES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
1992; 13 (4): 11311141
View details for Web of Science ID A1992JQ32900009

2 CHARACTERIZATIONS OF SUFFICIENT MATRICES
LINEAR ALGEBRA AND ITS APPLICATIONS
1992; 170: 6574
View details for Web of Science ID A1992HT97600005

THE PRINCIPAL PIVOTING METHOD REVISITED
MATHEMATICAL PROGRAMMING
1990; 48 (3): 369385
View details for Web of Science ID A1990EE53500003

SUFFICIENT MATRICES AND THE LINEAR COMPLEMENTARITYPROBLEM
LINEAR ALGEBRA AND ITS APPLICATIONS
1989; 114: 231249
View details for Web of Science ID A1989T835400016

A CONSTRUCTIVE CHARACTERIZATION OF Q0MATRICES WITH NONNEGATIVE PRINCIPAL MINORS
MATHEMATICAL PROGRAMMING
1987; 37 (2): 223231
View details for Web of Science ID A1987G701800006

A LAGRANGEAN RELAXATION ALGORITHM FOR THE CONSTRAINED MATRIX PROBLEM
NAVAL RESEARCH LOGISTICS
1986; 33 (1): 5576
View details for Web of Science ID A1986AYD2500005

ON THE UNIQUENESS OF SOLUTIONS TO LINEAR COMPLEMENTARITYPROBLEMS
MATHEMATICAL PROGRAMMING
1983; 27 (2): 191213
View details for Web of Science ID A1983RL34400005

MINIMAL TRIANGULATION OF THE 4CUBE
DISCRETE MATHEMATICS
1982; 40 (1): 2529
View details for Web of Science ID A1982NV44900004

ON THE CONVERGENCE OF A BLOCK SUCCESSIVE OVERRELAXATION METHOD FOR A CLASS OF LINEAR COMPLEMENTARITYPROBLEMS
MATHEMATICAL PROGRAMMING STUDY
1982; 17 (APR): 126138
View details for Web of Science ID A1982NR90200010

ON SPHERICALLY CONVEXSETS AND QMATRICES
LINEAR ALGEBRA AND ITS APPLICATIONS
1981; 41 (DEC): 7380
View details for Web of Science ID A1981MS80800004

OBSERVATIONS ON A CLASS OF NASTY LINEAR COMPLEMENTARITYPROBLEMS
DISCRETE APPLIED MATHEMATICS
1980; 2 (2): 89111
View details for Web of Science ID A1980JY26000001

LEASTINDEX RESOLUTION OF DEGENERACY IN QUADRATICPROGRAMMING
MATHEMATICAL PROGRAMMING
1980; 18 (2): 127137
View details for Web of Science ID A1980JN75300002

MANAGEMENT MODEL OF A GROUNDWATER SYSTEM WITH A TRANSIENT POLLUTANT SOURCE
WATER RESOURCES RESEARCH
1979; 15 (5): 12431249
View details for Web of Science ID A1979HS86500034

ALGORITHMIC EQUIVALENCE IN QUADRATIC PROGRAMMING .1. LEASTDISTANCE PROGRAMMING PROBLEM
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
1979; 28 (3): 275301
View details for Web of Science ID A1979HL63000001

SOLVING LINEAR COMPLEMENTARITY PROBLEMS AS LINEAR PROGRAMS
MATHEMATICAL PROGRAMMING STUDY
1978; 7 (FEB): 88107
View details for Web of Science ID A1978ES18500007

SOLUTION OF LARGE, STRUCTURED LINEAR COMPLEMENTARITY PROBLEMS  BLOCK PARTITIONED CASE
APPLIED MATHEMATICS AND OPTIMIZATION
1978; 4 (4): 347363
View details for Web of Science ID A1978GA22000003

SOLUTION OF LARGE, STRUCTURED LINEAR COMPLEMENTARITY PROBLEMS  TRIDIAGONAL CASE
APPLIED MATHEMATICS AND OPTIMIZATION
1977; 3 (4): 321340
View details for Web of Science ID A1977DZ11600002