Submodular Functions, Optimization, and Applications to Machine Learning — Spring Quarter, Lecture 1 —
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Algorithmic System Design Under Consideration of Dynamic Processes
Algorithmic System Design under Consideration of Dynamic Processes Vom Fachbereich Maschinenbau an der Technischen Universit¨atDarmstadt zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation vorgelegt von Dipl.-Phys. Lena Charlotte Altherr aus Karlsruhe Berichterstatter: Prof. Dr.-Ing. Peter F. Pelz Mitberichterstatter: Prof. Dr. rer. nat. Ulf Lorenz Tag der Einreichung: 19.04.2016 Tag der m¨undlichen Pr¨ufung: 24.05.2016 Darmstadt 2016 D 17 Vorwort des Herausgebers Kontext Die Produkt- und Systementwicklung hat die Aufgabe technische Systeme so zu gestalten, dass eine gewünschte Systemfunktion erfüllt wird. Mögliche System- funktionen sind z.B. Schwingungen zu dämpfen, Wasser in einem Siedlungsgebiet zu verteilen oder die Kühlung eines Rechenzentrums. Wir Ingenieure reduzieren dabei die Komplexität eines Systems, indem wir dieses gedanklich in überschaubare Baugruppen oder Komponenten zerlegen und diese für sich in Robustheit und Effizienz verbessern. In der Kriegsführung wurde dieses Prinzip bereits 500 v. Chr. als „Teile und herrsche Prinzip“ durch Meister Sun in seinem Buch „Die Kunst der Kriegsführung“ beschrieben. Das Denken in Schnitten ist wesentlich für das Verständnis von Systemen: „Das wichtigste Werkzeug des Ingenieurs ist die Schere“. Das Zusammenwirken der Komponenten führt anschließend zu der gewünschten Systemfunktion. Während die Funktion eines technischen Systems i.d.R. nicht verhan- delbar ist, ist jedoch verhandelbar mit welchem Aufwand diese erfüllt wird und mit welcher Verfügbarkeit sie gewährleistet wird. Aufwand und Verfügbarkeit sind dabei gegensätzlich. Der Aufwand bemisst z.B. die Emission von Kohlendioxid, den Energieverbrauch, den Materialverbrauch, … die „total cost of ownership“. Die Verfügbarkeit bemisst die Ausfallzeiten, Lebensdauer oder Laufleistung. Die Gesell- schaft stellt sich zunehmend die Frage, wie eine Funktion bei minimalem Aufwand und maximaler Verfügbarkeit realisiert werden kann. -
54 OP08 Abstracts
54 OP08 Abstracts CP1 Dept. of Mathematics Improving Ultimate Convergence of An Aug- [email protected] mented Lagrangian Method Optimization methods that employ the classical Powell- CP1 Hestenes-Rockafellar Augmented Lagrangian are useful A Second-Derivative SQP Method for Noncon- tools for solving Nonlinear Programming problems. Their vex Optimization Problems with Inequality Con- reputation decreased in the last ten years due to the com- straints parative success of Interior-Point Newtonian algorithms, which are asymptotically faster. In the present research We consider a second-derivative 1 sequential quadratic a combination of both approaches is evaluated. The idea programming trust-region method for large-scale nonlin- is to produce a competitive method, being more robust ear non-convex optimization problems with inequality con- and efficient than its ”pure” counterparts for critical prob- straints. Trial steps are composed of two components; a lems. Moreover, an additional hybrid algorithm is defined, Cauchy globalization step and an SQP correction step. A in which the Interior Point method is replaced by the New- single linear artificial constraint is incorporated that en- tonian resolution of a KKT system identified by the Aug- sures non-accent in the SQP correction step, thus ”guiding” mented Lagrangian algorithm. the algorithm through areas of indefiniteness. A salient feature of our approach is feasibility of all subproblems. Ernesto G. Birgin IME-USP Daniel Robinson Department of Computer Science Oxford University [email protected] -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
The Traveling Preacher Problem, Report No
Discrete Optimization 5 (2008) 290–292 www.elsevier.com/locate/disopt The travelling preacher, projection, and a lower bound for the stability number of a graph$ Kathie Camerona,∗, Jack Edmondsb a Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5 b EP Institute, Kitchener, Ontario, Canada N2M 2M6 Received 9 November 2005; accepted 27 August 2007 Available online 29 October 2007 In loving memory of George Dantzig Abstract The coflow min–max equality is given a travelling preacher interpretation, and is applied to give a lower bound on the maximum size of a set of vertices, no two of which are joined by an edge. c 2007 Elsevier B.V. All rights reserved. Keywords: Network flow; Circulation; Projection of a polyhedron; Gallai’s conjecture; Stable set; Total dual integrality; Travelling salesman cost allocation game 1. Coflow and the travelling preacher An interpretation and an application prompt us to recall, and hopefully promote, an older combinatorial min–max equality called the Coflow Theorem. Let G be a digraph. For each edge e of G, let de be a non-negative integer. The capacity d(C) of a dicircuit C means the sum of the de’s of the edges in C. An instance of the Coflow Theorem (1982) [2,3] says: Theorem 1. The maximum cardinality of a subset S of the vertices of G such that each dicircuit C of G contains at most d(C) members of S equals the minimum of the sum of the capacities of any subset H of dicircuits of G plus the number of vertices of G which are not in a dicircuit of H. -
A. Schrijver, Honorary Dmath Citation (PDF)
A. Schrijver, Honorary D. Math Citation Honorary D. Math Citation for Lex Schrijver University of Waterloo Convocation, June, 2002 Mr. Chancellor, I present Alexander Schrijver. One of the world's leading researchers in discrete optimization, Alexander Schrijver is also recognized as the subject's foremost scholar. A typical problem in discrete optimization requires choosing the best solution from a large but finite set of possibilities, for example, the best order in which a salesperson should visit clients so that the route travelled is as short as possible. While ideally we would like to have an efficient procedure to find the best solution, a famous result of the 1970s showed that for very many discrete optimization problems, there is little hope to compute the best solution quickly. In 1981, Alexander Schrijver and his co-workers, Groetschel and Lovasz, revolutionized the field by providing a powerful general tool to identify problems for which efficient procedures do exist. Professor Schrijver's record of establishing groundbreaking results is complemented by an almost legendary reputation for finding clearer, more compact derivations of results of others. This ability, together with high standards of mathematical rigour and historical accuracy, has made him the leading scholar in discrete optimization. His 1986 book, Theory of Linear and Integer Programming, is a landmark, and his forthcoming three- volume work on combinatorial optimization will certainly become one as well. Alexander Schrijver was born and educated in Amsterdam. Since 1989 he has worked at CWI, the National Research Institute for Mathematics and Computer Science of the Netherlands. He is also Professor of Mathematics at the University of Amsterdam. -
Submodular Functions, Optimization, and Applications to Machine Learning — Spring Quarter, Lecture 11 —
Submodular Functions, Optimization, and Applications to Machine Learning | Spring Quarter, Lecture 11 | http://www.ee.washington.edu/people/faculty/bilmes/classes/ee596b_spring_2016/ Prof. Jeff Bilmes University of Washington, Seattle Department of Electrical Engineering http://melodi.ee.washington.edu/~bilmes May 9th, 2016 f (A) + f (B) f (A B) + f (A B) Clockwise from top left:v Lásló Lovász Jack Edmonds ∪ ∩ Satoru Fujishige George Nemhauser ≥ Laurence Wolsey = f (A ) + 2f (C) + f (B ) = f (A ) +f (C) + f (B ) = f (A B) András Frank r r r r Lloyd Shapley ∩ H. Narayanan Robert Bixby William Cunningham William Tutte Richard Rado Alexander Schrijver Garrett Birkho Hassler Whitney Richard Dedekind Prof. Jeff Bilmes EE596b/Spring 2016/Submodularity - Lecture 11 - May 9th, 2016 F1/59 (pg.1/60) Logistics Review Cumulative Outstanding Reading Read chapters 2 and 3 from Fujishige's book. Read chapter 1 from Fujishige's book. Prof. Jeff Bilmes EE596b/Spring 2016/Submodularity - Lecture 11 - May 9th, 2016 F2/59 (pg.2/60) Logistics Review Announcements, Assignments, and Reminders Homework 4, soon available at our assignment dropbox (https://canvas.uw.edu/courses/1039754/assignments) Homework 3, available at our assignment dropbox (https://canvas.uw.edu/courses/1039754/assignments), due (electronically) Monday (5/2) at 11:55pm. Homework 2, available at our assignment dropbox (https://canvas.uw.edu/courses/1039754/assignments), due (electronically) Monday (4/18) at 11:55pm. Homework 1, available at our assignment dropbox (https://canvas.uw.edu/courses/1039754/assignments), due (electronically) Friday (4/8) at 11:55pm. Weekly Office Hours: Mondays, 3:30-4:30, or by skype or google hangout (set up meeting via our our discussion board (https: //canvas.uw.edu/courses/1039754/discussion_topics)). -
Curriculum Vitae Martin Groetschel
MARTIN GRÖTSCHEL detailed information at http://www.zib.de/groetschel Date / Place of birth: Sept. 10, 1948, Schwelm, Germany Family: Married since 1976, 3 daughters Affiliation: Full Professor at President of Technische Universität Berlin (TU) Zuse Institute Berlin (ZIB) Institut für Mathematik Takustr. 7 Str. des 17. Juni 136 D-14195 Berlin, Germany D-10623 Berlin, Germany Phone: +49 30 84185 210 Phone: +49 30 314 23266 E-mail: [email protected] Selected (major) functions in scientific organizations and in scientific service: Current functions: since 1999 Member of the Executive Committee of the IMU since 2001 Member of the Executive Board of the Berlin-Brandenburg Academy of Science since 2007 Secretary of the International Mathematical Union (IMU) since 2011 Chair of the Einstein Foundation, Berlin since 2012 Coordinator of the Forschungscampus Modal Former functions: 1984 – 1986 Dean of the Faculty of Science, U Augsburg 1985 – 1988 Member of the Executive Committee of the MPS 1989 – 1996 Member of the Executive Committee of the DMV, President 1992-1993 2002 – 2008 Chair of the DFG Research Center MATHEON "Mathematics for key technologies" Scientific vita: 1969 – 1973 Mathematics and economics studies (Diplom/master), U Bochum 1977 PhD in economics, U Bonn 1981 Habilitation in operations research, U Bonn 1973 – 1982 Research Assistant, U Bonn 1982 – 1991 Full Professor (C4), U Augsburg (Chair for Applied Mathematics) since 1991 Full Professor (C4), TU Berlin (Chair for Information Technology) 1991 – 2012 Vice president of Zuse Institute Berlin (ZIB) since 2012 President of ZIB Selected awards: 1982 Fulkerson Prize of the American Math. Society and Math. Programming Soc. -
Basic Polyhedral Theory 3
BASIC POLYHEDRAL THEORY VOLKER KAIBEL A polyhedron is the intersection of finitely many affine halfspaces, where an affine halfspace is a set ≤ n H (a, β)= x Ê : a, x β { ∈ ≤ } n n n Ê Ê for some a Ê and β (here, a, x = j=1 ajxj denotes the standard scalar product on ). Thus, every∈ polyhedron is∈ the set ≤ n P (A, b)= x Ê : Ax b { ∈ ≤ } m×n of feasible solutions to a system Ax b of linear inequalities for some matrix A Ê and some m ≤ n ′ ′ ∈ Ê vector b Ê . Clearly, all sets x : Ax b, A x = b are polyhedra as well, as the system A′x = b∈′ of linear equations is equivalent{ ∈ the system≤ A′x }b′, A′x b′ of linear inequalities. A bounded polyhedron is called a polytope (where bounded≤ means− that≤ there − is a bound which no coordinate of any point in the polyhedron exceeds in absolute value). Polyhedra are of great importance for Operations Research, because they are not only the sets of feasible solutions to Linear Programs (LP), for which we have beautiful duality results and both practically and theoretically efficient algorithms, but even the solution of (Mixed) Integer Linear Pro- gramming (MILP) problems can be reduced to linear optimization problems over polyhedra. This relationship to a large extent forms the backbone of the extremely successful story of (Mixed) Integer Linear Programming and Combinatorial Optimization over the last few decades. In Section 1, we review those parts of the general theory of polyhedra that are most important with respect to optimization questions, while in Section 2 we treat concepts that are particularly relevant for Integer Programming. -
1. Introduction: Learning About Operations Research
1. Introduction: Learning about Operations Research IRV LUSTIG: So hi, my name's Irv Lustig from Princeton Consultants and today, I'm privileged to interview George Nemhauser, who is currently a distinguished professor at the Georgia Institute of Technology. So thank you, George, for joining us today and let's get started. GEORGE NEMHAUSER: Oh, you're most welcome. I'm really looking forward to it. IRV LUSTIG: All right. So tell me, when did you first learn about operations research? GEORGE NEMHAUSER: So basically, I am a chemical engineer. And I think it was the summer between when I graduated with a Bachelor's degree in Chemical Engineering and the fall, when I was going to go off to graduate school at Northwestern for Chemical Engineering, I had a job with the research department of Allied Chemical. And there was a guy-- I think he was my supervisor who was working there-- who told me he was taking a part-time degree at Princeton and he was studying things like linear programming and game theory and I think maybe Kuhn, Tucker conditions, And he told me about this kind of stuff and I thought, wow, this is really interesting stuff, much more interesting than what I'm doing in chemical engineering. So when I got to Northwestern, as a first-year graduate student in Chemical Engineering, I had one elective course. And I looked and there was this new course called Operations Research and it included linear programming and game theory and stuff like that. I said, that's it. -
The Travelling Preacher, Projection, and a Lower Bound for the Stability Number of a Graph$
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Discrete Optimization 5 (2008) 290–292 www.elsevier.com/locate/disopt The travelling preacher, projection, and a lower bound for the stability number of a graph$ Kathie Camerona,∗, Jack Edmondsb a Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5 b EP Institute, Kitchener, Ontario, Canada N2M 2M6 Received 9 November 2005; accepted 27 August 2007 Available online 29 October 2007 In loving memory of George Dantzig Abstract The coflow min–max equality is given a travelling preacher interpretation, and is applied to give a lower bound on the maximum size of a set of vertices, no two of which are joined by an edge. c 2007 Elsevier B.V. All rights reserved. Keywords: Network flow; Circulation; Projection of a polyhedron; Gallai’s conjecture; Stable set; Total dual integrality; Travelling salesman cost allocation game 1. Coflow and the travelling preacher An interpretation and an application prompt us to recall, and hopefully promote, an older combinatorial min–max equality called the Coflow Theorem. Let G be a digraph. For each edge e of G, let de be a non-negative integer. The capacity d(C) of a dicircuit C means the sum of the de’s of the edges in C. An instance of the Coflow Theorem (1982) [2,3] says: Theorem 1. The maximum cardinality of a subset S of the vertices of G such that each dicircuit C of G contains at most d(C) members of S equals the minimum of the sum of the capacities of any subset H of dicircuits of G plus the number of vertices of G which are not in a dicircuit of H. -
N Rapid Development of an Open-Source Minlp Solver With
75 o N O PTIMA Mathematical Programming Society Newsletter DECEMBER 2007 Rapid Development of an Open-source Minlp Solver with COIN-OR Pierre Bonami, John J. Forrest, Jon Lee and Andreas Wächter Abstract • Csdp, Dfo, Ipopt, LaGO, and Svm- QP are solvers for different types of We describe the rapid development of Nonlinear Optimization (semidefinite, Bonmin (Basic Open-source Nonlinear derivative-free, general large-scale Mixed INteger programming) using the interior point, global optimization, QP community and components of COIN- solver for support vector machines) OR (COmputational INfrastructure • CoinMP, FlopC++, GAMSlinks, for Operations Research). NLPAPI, Osi, OS and Smi are problem 1. Introduction modeling and interface tools. Even more, COIN-OR has become the As famous examples like Linux have platform that facilitates the collaboration proven, open-source communities of optimization researchers to start entirely can produce rapidly-developing high- new projects, exploring and developing new quality software, often competitive with algorithmic ideas, by providing both a sound expensive commercial solutions. COIN- software basis that can be re-used, as well as OR (COmputational INfrastructure the technical forum to coordinate the effort. for Operations Research), originally In order to clarify a common founded by IBM in 2000 and a non-profit misconception, we want to emphasize that foundation since 2004, provides such the term “open source” does not simply refer a platform for us optimization folks. to software that is made available to some Since its conception, a number of users in source-code format. According optimization-algorithm implementations to the definition put forth by the non- and related software projects have been profit corporation Open Source Initiative contributed to COIN-OR. -
Branch-And-Bound Strategies for Dynamic Programming
LIBRARY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY C7. WORKING PAPER ALFRED P. SLOAN SCHOOL OF MANAGEMENT BRANCH-AND-BOUND STRATEGIES FOR DYNAMIC PROGRAMMING Thomas L. Morin* and Roy E. Marsten** WP 750-74ooREVISED May 1975 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 50 MEMORIAL DRIVE CAMBRIDGE, MASSACHUSETTS 02139 BRANCH-AND-BOUND STRATEGIES FOR DYNAMIC PROGRAMMING Thomas L. Morin* and Roy E. Mar St en** WP 750-74floREVISED May 1975 *Northwestern University, Evanston, Illinois **Massachusetts Institute of Technology Alfred P. Sloan School of Management, Cambridge, Massachusetts ABSTRACT This paper shows how branch -and -bound methods can be used to reduce storage and, possibly, computational requirements in discrete dynamic programs. Relaxations and fathoming cjriteria are used to identify and to eliminate states whose corresponding subpolicies could not lead to optimal policies. The general dynamic programming/branch- and-bound approach is applied to the traveling -salesman problem and the nonlinear knapsack problem. The reported computational experience de- monstrates the dramatic savings in both computer storage and computa- tional requirements which were effected utilizing the hybrid approach. Consider the following functional equation of dynamic programming for additive costs: = {TT(y',d) (y = (P. - f(y) min + f ') lT(y ' ,d) y] , y € y.) (1) d € D with the boundary condition f(yo) = ko (2) in which, Q is the finite nonempty state space; y- € fi is the initial state; d € D is a decision, where D is the finite nonempty set of decisions; T: n X D — n is the transition mapping, where T(y',d) is the state that is tt; -• reached when decision d is applied at state y ; Q x D IR is the cost function, where TT(y',d) is the incremental cost that is incurred when de- cision d is applied at state y'; k_ 6 IR is the initial cost incurred in the initial state y_; and in (2) we make the convenient but unnecessary assump- tion that return to the initial state is not possible.