21. Computational Geometry, Algorithms And Applications Recent book with a focus on applications, by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Includes chapters on linesegment intersection, polygon triangulation, linear programming, range searching, point location, Voronoi diagrams, arrangements and duality, Delaunay triangulations, geometric data structures, convex hulls, binary space partitions, robot motion planning, visibility graphs. http://www.cs.ruu.nl/geobook/

About the book Cover Table of contents Errata (1st edition) Errata (2nd edition) ... Order Implementation CGAL LEDA More software Further reading Books Bibliography Web sites Comments to geobook@cs.uu.nl Last modified Oct 9, 2000 Computational Geometry: Algorithms and Applications Second Edition Mark de Berg Otfried Schwarzkopf TU Eindhoven (the Netherlands) Marc van Kreveld Mark Overmars Utrecht University (the Netherlands) published by Springer-Verlag 2nd rev. ed. 2000. 367 pages, 370 fig. Hardcover DM 59 ISBN: 3-540-65620-0 You can order the book here This textbook on computational geometry has 367 pages. The pages are almost square with a large margin containing over 370 figures. To get an idea about the style and format, take a look at the Introduction or chapter 7 on Voronoi diagrams Computational geometry Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains-computer graphics, geographic information systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self study.

22. OR/MS Today - LINEAR PROGRAMMING SOFTWARE SURVEY OR/MS Today 2001 linear programming SOFTWARE SURVEY Be sure to take a look at the companion article to this survey linear programming by Robert Fourer. http://www.lionhrtpub.com/orms/surveys/LP/LP-survey.html

OR/MS Today 2001 LINEAR PROGRAMMING SOFTWARE SURVEY The information in this survey was provided by the vendors in response to a questionnaire developed by Robert Fourer. The survey should not be considered as comprehensive, but rather as a representation of available Linear Programming packages. Questionnaires were sent to 60 vendors drawn from previous survey participants, the OR/MS Today database and other sources. It includes the products of those vendors who responded by July 1, 2001. If you know of a Linear Programming package that is not in this survey, please contact Jennie Farnsworth at (770) 431-0867, ext. 225 or e-mail them to jen@lionhrtpub.com . They will be included in the online version. The survey is broken down into nine separate tables (plus a vendor contact list) for easier downloading and viewing: Table 1: Software Description: Type: Form: Independent Application, Callable Library, Source Code, Add-in to General-purpose Software Table 2: Platforms Supported: DOS, PC/Windows (95, 97, NT), LINUX, UNIX, Mac OS, Other (specify) Multiprocessor Support: Shared Memory, Distributed Memory

23. OR/MS Today - LINEAR PROGRAMMING SOFTWARE SURVEY OR/MS Today 2003 linear programming SOFTWARE SURVEY Be sure to take a look at the companion article to this survey linear programming by Robert Fourer. http://www.lionhrtpub.com/orms/surveys/LP/LP-surveymain.html

OR/MS Today 2003 LINEAR PROGRAMMING SOFTWARE SURVEY The information in this survey was provided by the vendors in response to a questionnaire developed by Robert Fourer. The survey should not be considered as comprehensive, but rather as a representation of available Linear Programming packages. Questionnaires were sent to 60 vendors drawn from previous survey participants, the OR/MS Today database and other sources. It includes the products of those vendors who responded by Nov. 1. If you know of a Linear Programming package that is not in this survey, please contact Patton McGinley at (770) 431-0867, ext. 214 or e-mail them to patton@lionhrtpub.com . They will be included in an online version. UPDATES: The survey is broken down into ten separate tables (plus a vendor contact list) for easier downloading and viewing: Table 1: Characteristics: Table 2: Interfaces: Callable Library, Object/Class Library, Source Code, Add-in To Table 3: Interfaces (continued): Data Compatibility (Reads Spreadsheets, Writes Spreadsheets, Reads Database, Writes Database, Reads and Writes Text) Table 4: Platforms Supported: Windows, Linux, Solaris, Mac OS, Others

24. Linear Programming FAQ linear programming FAQ. There are reader questions on this topic! Help others by sharing your knowledge. What is linear programming? * Q2. http://www.faqs.org/faqs/linear-programming-faq/

Usenet FAQs Search Web FAQs Documents ... RFC Index Linear Programming FAQ There are reader questions on this topic! Help others by sharing your knowledge From: 4er@iems.nwu.edu (Robert Fourer) Newsgroups: sci.op-research 4er@iems.nwu.edu (Robert Fourer) Summary: A List of Frequently Asked Questions about Linear Programming Keywords: FAQ, LP, Linear Programming Posted-By: auto-faq 2.4 Archive-name: linear-programming-faq Last-modified: November 1, 1997 [ ] Linear Programming Frequently Asked Questions Optimization Technology Center of Northwestern University and Argonne National Laboratory [ ] Posted monthly to Usenet newsgroup sci.op-research World Wide Web version: http://www.mcs.anl.gov/home/otc/Guide/faq/linear-programming-faq.html michel@es.ele.tue.nl ) says has solved models with up to 30,000 variables and 50,000 constraints. The author requests that people retrieve it from ftp://ftp.es.ele.tue.nl/pub/lp_solve (numerical address at last check: 131.155.20.126). There is an older version to be found in the Usenet archives, but it contains bugs that have been fixed in the meantime, and hence is unsupported. The author also made available a program that converts data files from MPS-format into lp_solve's own input format; it's in the same directory, in file mps2eq_0.2.tar.Z. The documentation states that it is not public domain, and the author wants to discuss it with would-be commercial users. As an editorial opinion, I must state that difficult models will give lp_solve trouble; it's not as good as a commercial code. But for someone who isn't sure what kind of LP code is needed, it represents a reasonable first try. LP-Optimizer is a simplex-based code for linear and integer programs, written by Markus Weidenauer (

25. Linear Programming - Ignizio Cavalier linear programming by James P. Ignizio and Tom M. Cavalier, Prentice Hall International Series in Industrial and Systems Engineering, 666pp (1994). http://www.personal.psu.edu/tmc7/lpbook.html

26. Python Professional Services Mixed integer/linear programming modules. http://www.pythonpros.com/arw/pysimplex/

Notice: At this time, Python Professional Services is no longer accepting additional clients for support contracts, training, or custom software development. If you have any questions, please email: Greg Stein, PPSI President Please visit the main Python website for more information about Python. The PPSI Community Center remains available for use by the Python community. The Community Center hosts several Python-related mailing lists and CVS Repositories Last modified: Mon Jun 12 00:26:16 PDT 2000

27. RIOT: Interactive Linear Programming: Introduction Interactive linear programming. There has been a proliferation of linear programming solver software since 1980 (ex CPLEX, LINGO, MINOS, etc). http://ford.ieor.berkeley.edu/riot/Tools/InteractLP/

Interactive Linear Programming RIOT HOME Linear Programming What is LP? ... Linear Programming This portion of the RIOT site is still under construction. The navigational are "uneven" across the pages, and the editorial content is still being polished. Please bear with us during the consruction. Project Overview Objective: To create an interface between the WWW and a linear programming solver allow anyone with access to the Web to submit a linear program and have it solved. There has been a proliferation of linear programming solver software since 1980 (ex : CPLEX, LINGO, MINOS, etc). Each solver implements different algorithms (Simplex method, Interior-Point method, etc) and offers different options (sensititvity analysis, basic certificates, etc). Depending on the problem to be solved, some solvers can be more or less efficient than other in terms of speed, accuracy, number of iterations and available options. The first step of our project will be to create an interface between a linear programming solver and the web so that a user can submit his problem through the internet in order to have it solved.

28. RIOT - Operations Research Tools linear programming, Try out small linear programming models using an interactive input interface. Automatically generate graphical http://ford.ieor.berkeley.edu/riot/Tools/

Operations Research Tools RIOT HOME Tools: Linear Programming About Riot ... Linear Programming Try out small linear programming models using an interactive input interface. Automatically generate graphical solutions to two-dimensional problems. Linear Programming RIOT HOME

29. Energy And Materials Policy Design linear programming models for environmental policy analysis, with emphasis on CO2 policies. Focus on trade effects, technological change, data, publications, model code. Covers iron and steel, petrochemicals, waste, biomass. http://www.resourcemodels.org/

Something completely different: Fossil reptiles (Updated with some dinosaur and croc finds 22/5/2004) NEW: the IEA ETP model The Energy Technology Perspectives model is a new world energy systems model. See also the IEA website May 2004 Transportation in the World and the EU. A bird's eye view April 2004 Energy efficiency and eco-efficiency: The IEA ETP model March 2004 The hydrogen economy: an IEA-ETP perspective December 2003 IEA ETP results for China, with emphasis on the Chinese industry November 2003 The future role of CO2 capture and storage. Results of the IEA-ETP model October 2003 Challenges in energy and environment modelling: a materials perspective This site focuses on energy and materials modelling for policy analysis. Energy and CO2 policies, waste treatment, land use, technology assessment and international trade (leakage effects) are some of the issue that are discussed. The models presented have been developed at the International Energy Agency (IEA) in Paris and the National Institute for Environmental Studies (NIES) in Tsukuba, Japan. This site contains data on technologies that are of interest for energy, CO2 emissions and waste decision making. Click on the links in the table below in order to get more information regarding a specific materials/activity category. The models on this website have been developed from a systems engineering perspective: the economy is a network of processes that are linked via flows of energy and materials and monetary flows. Processes and flows can be changed if appropriate measures are taken. Processes and flows are characterized by a limited number of variables. The number of variables in the model exceeds the number of relations (equations) among the variables. An objective function is defined which is minimized or maximized (in this case, the system costs are minimized) or the consumer/producer surplus is maximised.

30. Summary Linear Programming linear programming (LP) Problem The graphical method for solving linear programming problems in two unknowns is as follows. A. Graph the feasible region. http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Summary4.html

Summary of Chapter 4 in Finite Mathematics and Topic: Linear Programming Return to Main Page True/False Quiz Review Exercises On-Line Tutorial ... Everything for Calculus Chapter 3 Summary Chapter 5 Summary Utilities: Linear Programming Grapher Pivot and Gauss-Jordan Tool Excel Pivot and Gauss-Jordan Tool Simplex Method Tool ... Simplex Method for Minimization Problem Linear Programming (LP) Problem A linear programming problem is one in which we are to find the maximum or minimum value of a linear expression ax + by + cz + . . . (called the objective function ), subject to a number of linear constraints of the form Ax + By + Cz + . . . N or Ax + By + Cz + . . . N. The largest or smallest value of the objective function is called the optimal value , and a collection of values of x, y, z, . . . that gives the optimal value constitutes an optimal solution . The variables x, y, z, . . . are called the decision variables Example Here is an example of an LP problem: Find the maximum value of p = 3x subject to z x + 2y + z x 0, y 0, z

31. Compuchem Consultants Suppliers of engineering services, software products for linear programming modeling, and IT Services http://www.compuchem.net

32. Linear Programming Grapher (Two Variables) linear programming Grapher (Two Variables) a Utility for Finite Mathematics (2e). Enter the linear programming problem here. Xmin http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/LPGrapher/lpg.html

Linear Programming Grapher (Two Variables) a Utility for Finite Mathematics (2e) Return to Main Page More On-Line Utilities Topic Summary for Linear Programming ... Everything for Finite Math Use of this system is pretty intuitive. Enter your linear programming problem (with two variables x and y) in the space below, and press "Solve" to solve without showing the feasible region, or "Graph" to solve it and also show the feasible region for your problem. Press "Example" to see an example of a linear programming problem already set up. To solve a linear programming problem with more than two unknowns, use the Simplex Method Tool In some browsers, you might have to jiggle the graph window size a little to make the graph appear. Solution Display Some browsers (including some versions of Internet Explorer) use a sans serif proportional width font in text boxes. This will cause the display of solutions to appear a little messy. You can remedy this by changing the "Sans Serif" font in your browser preferences to "Courier" or some other fixed-width font, and then reloading the page. Warning The graphing routine will tax your browser, and it might crash and cause your computer to crash with it. Thus

33. Home Page Uses techniques to measure financial risk, optimize staffing, and predict wait times. Customized analyses and training feature Monte Carlo simulation, linear programming, and queuing models. http://www.calculatedriskinc.com/

34. [B/D] - The Bayes Linear Programming Language B/D The Bayes linear programming Language. Welcome to the home of B/D. From this page, you can download the B/D software, and http://fourier.dur.ac.uk:8000/stats/bd/

[B/D] - The Bayes Linear Programming Language Welcome to the home of [B/D]. From this page, you can download the [B/D] software, and accompanying documentation. In time it will also contain update release notes, macro libraries, etc. To run the software you will need to take either the co-processor or the no-coprocessor version of the main program from the [B/D] for Windows link. Neither of these files contain documentation. You will almost certainly have to read some documentation. Sorry about that. Three tutorial guides and a reference manual are supplied in various formats - follow the [B/D] Documentation link to find them. The [B/D] manual is also available online in html format, as [B/D] manual online . Your best bet is to read the document entitled Bayes linear methods II in conjunction with the document Bayes linear methods I , which sets out the basic theory, concepts, and notation. Before you take anything, be warned! [B/D] supplies tools to help you organise and analyse your beliefs and data. You cannot use it without thinking, and it does not contain the usual statistical macros. If you're looking for a package to apply, for example, standard linear regression mindlessly, look elsewhere. See the Bayes linear home page for more details.

35. Linear Programming -- From MathWorld linear programming. linear programming, also polyhedron. linear programming is extensively used in economics and engineering. Examples from http://mathworld.wolfram.com/LinearProgramming.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Applied Mathematics Optimization Linear Programming Linear programming, also known as operations research optimization theory convex optimization theory , or linear optimization, is the problem of maximizing a linear function over a convex polyhedron. Linear programming is extensively used in economics and engineering. Examples from economics include Leontief's input-output model, the determination of shadow prices, etc., while an example of an engineering application would be maximizing profit in a factory that manufactures a number of different products from the same raw material using the same resources. Linear programming can be solved using the simplex method (Wood and Dantzig 1949, Dantzig 1949) which runs along polytope edges of the visualization solid to find the best answer. Khachian (1979) found a

36. Vanguard DecisionPro Software for business decision analysis and forecasting. Supports decision tree analysis, Monte Carlo simulation, linear programming, forecasting, Markov trees, expert systems, and general business modeling. http://www.vanguardsw.com/decisionpro/

Home Search Products Order ... Vanguard DecisionPro Introduction to DecisionPro Make Better Decisions Keep Pace With Your Competitors Communicate Your Ideas ... Trial Software Brochure DecisionPro Brochure (PDF) Resources System Requirements Pricing Reseller Program Customers 1 of 6 DecisionPro picks up where your spreadsheet leaves off ... It helps you make the best possible business decisions by applying proven management techniques such as: decision tree analysis, Monte Carlo simulation, linear programming, and advanced forecasting methods. It gives you unprecedented power and flexibility by integrating all of the key quantitative methods in management into a single application. What's more, DecisionPro's innovative interface makes this power so easy to apply that you will find yourself using it even for routine problems. See how DecisionPro can help you make better decisions and communicate your ideas with impact, download the FREE trial software . If you have questions, please call

37. LP_SOLVE Linear Programming Code LP_SOLVE linear programming Code. FTP site for lp_solve; Mail to author Michel Berkelaar; linear programming FAQ; Download Files (local site) Problem Links. http://www.cs.sunysb.edu/~algorith/implement/lpsolve/implement.shtml

LP_SOLVE: Linear Programming Code The non-commercial linear programming code of choice appears to be , written in ANSI C by Michel Berkelaar, who claims to have solved problems as large as 30,000 variables and 50,000 constraints. Lp_solve can also handle (smaller) integer and mixed-integer problems. It is available by anonymous ftp from ftp://ftp.es.ele.tue.nl/pub/lp_solve, but is not in the public domain. A user community for lp_solve exists, which has ported it to a variety of different platforms. FTP site for lp_solve Mail to author Michel Berkelaar Linear Programming FAQ Download Files (local site) Problem Links Linear Programming (9) Post comments Read comments View the statistics for this implementation ... The Stony Brook Algorithm Repository go to front page This page last modified on Apr 29, 1996.

38. 1.2.6 Linear Programming 1.2.6 linear programming. INPUT OUTPUT. Excerpt from The Algorithm Design Manual The standard algorithm for linear programming is called the simplex method. http://www.cs.sunysb.edu/~algorith/files/linear-programming.shtml

1.2.6 Linear Programming INPUT OUTPUT Input Description: A set of linear inequalities, a linear objective function. Problem: Find the assignment to the variables maximizing the objective function while satisfying all inequalities. Excerpt from The Algorithm Design Manual : The standard algorithm for linear programming is called the simplex method . Each constraint in a linear programming problem acts like a knife that carves away a region from the space of possible solutions. We seek the point within the remaining region that maximizes (or minimizes) $f(X)$. By appropriately rotating the solution space, the optimal point can always be made to be the highest point in the region. Since the region (simplex) formed by the intersection of a set of linear constraints is convex, we can find the highest point by starting from any vertex of the region and walking to a higher neighboring vertex. When there is no higher neighbor, we are at the highest point. While the basic simplex algorithm is not too difficult to program, there is a considerable art to producing an efficient implementation capable of solving large linear programs. For example, large programs tend to be sparse (meaning that most inequalities use few variables), so sophisticated data structures must be used. There are issues of numerical stability and robustness, as well as which neighbor we should walk to next (so called pivoting rules ). Finally, there exist sophisticated

39. Dipartimento Di Informatica - Università Di Torino Department of Informatics. Research groups concentrate on knowledge representation and reasoning, machine learning, natural language processing, databases and information systems, decision making models and management systems, informatic technology, linear programming, integer linear programming, game theory, logic programming and automated reasoning, mathematical logic, performance analysis, modelling in biology and medicine, cooperative systems, multidimensional signal processing, security and computer networks, semantics and logics of computation. http://www.di.unito.it/

U S TUDI DI T ORINO phone number Il Dipartimento di Informatica aderisce allo STATO DI AGITAZIONE Information HowToReachUs People ... University home Administrator: wwwadm[at]di.unito.it Last update: 29 Apr 2004

40. GLPK - GNU Project - Free Software Foundation (FSF) GLPK (GNU linear programming Kit). image of the Head of a GNU. http://www.gnu.org/software/glpk/glpk.html

GLPK (GNU Linear Programming Kit) Introduction Get the Software Documentation Mailing Lists/Newsgroups ... Introduction to GLPK The GLPK ( G NU L inear P rogramming K it) package is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. GLPK supports the GNU MathProg language, which is a subset of the AMPL language. The GLPK package includes the following main components: Revised simplex method. Primal-dual interior point method. Branch-and-bound method. Translator for GNU MathProg. Application program interface (API). Stand-alone LP/MIP solver. Downloading GLPK The GLPK distribution can be found in the subdirectory /gnu/glpk/ on your favorite GNU mirror . For other ways to obtain GLPK, please read How to get GNU Software Documentation The GLPK documentation consists of the Reference Manual and the description of the GNU MathProg language. Both these documents are included in the distribution (in LaTeX, DVI, and PostScript formats). Mailing Lists/Newsgroups GLPK has two mailing lists: and The main discussion list is , and is used to discuss all aspects of GLPK, including its development and porting.

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