1. Linear Programming FAQ From the newsgroup sci.opresearch, maintained at the Optimization Technology Center of Northwestern Category Science Math Operations Research FAQs and Tutorials......linear programming Frequently Asked Questions. Optimization Technology Centerof application areas. Q1. What is linear programming? . A (For http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html

Linear Programming Frequently Asked Questions Optimization Technology Center of Northwestern University and Argonne National Laboratory Posted at http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html Changes posted to Usenet newsgroup sci.op-research Date of this version: January 1, 2003 What is Linear Programming Where is there good software to solve LP problems?" "Free" codes Commercial codes and modeling systems Free demos of commercial codes Q3. "Oh, and we also want to solve it as an integer program Q4. "I wrote an optimization code. Where are some test models Q5. "What is MPS format Topics briefly covered: : "What is a modeling language?" : "How do I diagnose an infeasible LP model?" : "I want to know the specific constraints that contradict each other." : "I just want to know whether or not a feasible solution exists : "I have an LP, except it's got several objective functions." : "I have an LP that has large almost-independent matrix blocks that are linked by a few constraints. Can I take advantage of this?" : "I am looking for an algorithm to compute the convex hull of a finite number of points in n-dimensional space."

2. Optimization Frequently Asked Questions Includes basic definitions and links to free and commercial software. http://www-unix.mcs.anl.gov/otc/Guide/faq/

Optimization Frequently Asked Questions Linear Programming FAQ Nonlinear Programming FAQ These FAQs were established by John W. Gregory and are currently being maintained by Robert Fourer 4er@iems.nwu.edu ) and the Optimization Technology Center of Argonne National Laboratory and Northwestern University. NEOS Guide NEOS Server Comments

3. Linear Programming Faq This page has moved to http// www unix. gov/ otc/ Guide/ faq/ linear- programming- faq. Please update your links. http://www.mcs.anl.gov/home/otc/Guide/faq/linear-programming-faq.html

This page has moved to http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html Please update your links.

4. Linear Programming Short Course Web sites with materials for linear programming, supporting the linear programming Short Course. This is a short course in linear programming (LP) designed for people who already know linear algebra and want to http://www.cudenver.edu/~hgreenbe/courseware/LPshort/intro.html

5. An Introduction To Linear Programming And The Simplex Algorithm No Title http://www.isye.gatech.edu/~spyros/LP/LP.html

Next: The LP formulation and An Introduction to Linear Programming and the Simplex Algorithm by Spyros Reveliotis Acknowledgements There are a number of people who have contributed during the inceptional and implementational phases of this project through constructive comments and discussions, provision of information and technical assistance. At this point, I would like to acknowledge their valuable aid. Hence, I would like to say a "big" THANKS to: Evangelia Dimaraki, Amy Pritchett, Bhaskar Manda, Darren Hunt, Victoria Burse, Randy Riegsecker, Balu Vandor, Javier Ruiz and Fangjun Zhou . Many thanks go also to my students of the past IE3231 classes , since it was my interaction with them that motivated and inspired this whole effort. I would also like to acknowledge the financial (and not only) support of the School of Industrial and Systems Engineering and the CETL group at the Georgia Institute of Technology The integrated software supporting the execution of interactive examples "re-uses" the very nice software modules developed by (i) Drs Ken Goldberg and Ilan Adler at the Dept. of Industrial Engineering and Operations Research

6. Linear Programming: Foundations And Extensions Book by Robert J. Vanderbei in PDF.Category Science Math Publications Online Texts......linear programming Foundations and Extensions. Book Cover Image Order.Table of Contents. Lecture Presentations for Chapters 2, 5, 13 http://www.princeton.edu/~rvdb/LPbook/

Linear Programming: Foundations and Extensions Order Table of Contents Lecture Presentations for Chapters 13 (intro) , and 13 (algorithms) (pdf format) (Note: the embedded hyperlinks work best if the pdf file is downloaded and viewed using acroread rather than a web browser; i.e., right-click is better than left-click.) Lecture Notes-Undergraduate level (pdf format) Lecture Notes-Graduate level (pdf format) Online version of 2nd Edition (note that the hyperlinks in the text really work) Associated software (C/C++ source code) Additional Exercises Online Exercises Errata Simple pivot tool (a java applet to help solve exercises from Chapters 1 to 5) Advanced pivot tool (a java applet to help solve exercises from Chapters 5 to 7) Online pivot exam (a java applet to evaluate your knowledge of the simplex method) The Network-Simplex Pivot Tool Intended Audience This book is an introductory graduate textbook on linear programming although upper-level graduate students and researchers will find plenty of material here that cannot be found in other books. It has also been used successfully to teach undergraduates majoring in Operations Research.

7. Mathematics Archives - Topics In Mathematics - Linear/Nonlinear Programming Linear / Nonlinear programming. Optimization. Advanced linear programming. ADD. KEYWORDS Sensitivity Analysis, Model http://archives.math.utk.edu/topics/linearProg.html

Topics in Mathematics Linear / Nonlinear Programming Optimization Advanced Linear Programming ADD. KEYWORDS: Sensitivity Analysis, Model Simplification, Graphs of Linear Programs, Embedded and Hidden Structures, Sparse Matrix Techniques for Simplex and Interior Methods, Course Notes AMS's Materials Organized by Mathematical Subject Classification - Economics, Operations Research, Programming, Games ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases Anima-LP: A Tool for Teaching Linear Programming Another Copy Annals of Operations Research ADD. KEYWORDS: Published Journal Bibliography on Interior Point Methods for Mathematical Programming CCC - Constraints Archive ADD. KEYWORDS: People, Bibliographies, Papers, Software, Benchmarks

8. A Mathematical Modeling Language Information on LPL, a mathematical modeling language, related product, projects and links. http://diufpc03.unifr.ch/lpl/lpl.html

A Mathematical Modeling System LPL Home What for? Highlights Products ... Contact Us Linear Programming Language LPL is a mathematical modeling system which can be used to build, modify, and document large mathematical models. The LPL modeling system has been successfully applied to large linear and mixed integer programs. A compiler translates models written in the LPL language to the input code of any LP/MIP solver, calls the solver automatically, reads the solution back to its internal representation, and writes user defined reports in form of tables. Logical Programming Language LPL is also a logical modeling language. One can formulate logical constraints. which are translated symbolically into mathematical constraints using 0-1 variables. Literate Programming Language LPL is a documentation language. One can generate automatically a LaTeX file from a large mathematical model. Last update: December 2, 2002, Tony Huerlimann

9. ABACUS ABACUS is a software system which provides a framework for the implementation of branchand-bound algorithms using linear programming relaxations that can be complemented with the dynamic generation of cutting planes or columns (branch-and-cut, branch-and-price,branch-and-cut-and-price). http://www.informatik.uni-koeln.de/ls_juenger/projects/abacus.html

ABACUS - A Branch-And-CUt System ABACUS is a software system which provides a framework for the implementation of branch-and-bound algorithms using linear programming relaxations that can be complemented with the dynamic generation of cutting planes or columns (branch-and-cut, branch-and-price, branch-and-cut-and-price). This system allows the software developer to concentrate merely on the problem specific parts, i.e., the cutting plane and column generation and the primal heuristics. Moreover, ABACUS provides a variety of general algorithmic concepts, e.g., enumeration and branching strategies, from which the user of the system can choose the best alternative for his application. Finally, ABACUS provides many basic data structures and useful tools for the implementation of such algorithms. ABACUS is designed both for general mixed integer optimization problems and for combinatorial optimization problems. It unifies cutting plane and column generation within one algorithm framework. Simple reuse of code and the design of abstract data structures and algorithms are essential for a software framework. These requirements are met by object oriented programming techniques. Therefore, ABACUS is implemented as a collection of C++ classes. Distributions ABACUS is distributed as a callable library together with an example and the documentation. We provide precompiled libraries for various UNIX platforms and Windows NT. The current version of ABACUS is release 2.2.

10. Optimization Frequently Asked Questions Optimization Frequently Asked Questions linear programming FAQ Nonlinear programming FAQ http://www.mcs.anl.gov/home/otc/Guide/faq

Optimization Frequently Asked Questions Linear Programming FAQ Nonlinear Programming FAQ These FAQs were established by John W. Gregory and are currently being maintained by Robert Fourer 4er@iems.nwu.edu ) and the Optimization Technology Center of Argonne National Laboratory and Northwestern University. NEOS Guide NEOS Server Comments

11. Calculate Feed Formulation Online By Linear Programming For All Animal All Stage Site has a program which will calculate feed formulation by linear programming for a fee. http://www.mixfeedonline.com/

Welcome to Mix Feed Online This web allow user calculate feed formulation by Linear Programming for Swine, Layer Hen, Broilers, Ducks, Geese, Turkeys, Quails, Ostrich, EMU, Beef and Dairy Cattle, Sheep, Goats, Dogs, Cats, Rabbits, Fish, Shrimp What's Mix Feed Online Mix Feed Online is the newest development of animal online mixed-feed web service in the internet . By using linear programming method , which is recognized and being use world wide by animal feed manufactures .Mix Feed Online give you the best web service . With the lowest cost , Mix Feed Online can give you the best mixed feed ingredients for your animals ( Swine ,Beef Cattle, Dairy cattle, Sheep, Goats, Broilers, Layers, Ducks, Geese, Turkeys, Ostrich, Emu, Bobwhite quail, Japanese quail, Ringneck quail ,Dogs, Cats, Rabbits, Fish, Shrimp ) , while you are sitting at home . Mix Feed Online can give you the manufacture quality animals mixed feed ingredients with the perfect nutrients(amino acid, vitamins, mineral, fatty acid, energy),raw material and the lowest cost . You can adjust the quality of the animal feed in your own way without limitation . Mix Feed Online is easily to use and can be learn in the short time with 100 % precision . Why Linear programming Animal feed production technology take the knowledge of operation research especially Linear Programming, in calculating the mixture of the feed , giving the perfect quality ‘s mixed feed ingredients for your animals .

12. Linear And Nonlinear Programming FAQs The FAQs for linear programming and Nonlinear programming have movedto a different site http//www.mcs.anl.gov/home/otc/Guide/faq/. http://www.skypoint.com/~ashbury/linear-programming-faq.html

The FAQs for Linear Programming and Nonlinear Programming have moved to a different site: http://www.mcs.anl.gov/home/otc/Guide/faq/

13. Optimization Using Excel Solver - Frontline Systems The company that developed the Solver in Microsoft Excel, the Solver in Lotus 12-3, and the Optimizer in Quattro Pro, now offers optimized versions of each of these, for goalseeking or backsolving, and constrained optimization using linear programming, nonlinear programming, and integer programming methods. http://www.frontsys.com/

Visit www.solver.com New Website for Frontline Systems! Developers of Your Spreadsheet's Solver Announcing the Premium Solver Platform Global Optimization, Hybrid Evolutionary/Classical Solver and Constraint Programming Enhancements C lassic L inea r I ntege r Programmin g and Nonline a r Optimizatio n And Field-Installable Solver Engin es to Solve Problems of Virtuall y Unlimited Size Download a Free Evaluation Version on our Private Web for Solver Users New Solver Engines for the Premium Solver Platform Large-Scale LP Solver Solves Linear Programming Problems up to 65,000 Variables Large-Scale GRG Solver S olves Nonlinear Optimization Pr o blems up to 4,000 Variables LGO Global Solver Solves Global Optimization Problems up to 1,000 Variables OptQuest Solver Solves Non-Smooth Optimization Problems up to 5,000 Variables Free Evaluation Versions Available for Download on our Private Web for Solver Users XPRESS Solver Engine for the Premium Solver Platform Lightning-Fast DEVELOPERS: Use our Solver DLL V3.5 in your own applications Download a FREE Solver DLL Evaluation Kit from our Private Web Our Basic Excel Solver Upgrade: Premium Solver V3.5

14. PCx Linear Programming Code Software for linear programming. PCx is an interiorpoint predictor-correctorlinear programming package. The code has been developed http://www.mcs.anl.gov/otc/Tools/PCx/

Software for Linear Programming PCx is an interior-point predictor-corrector linear programming package. The code has been developed at the Optimization Technology Center, which is a collaboration between Argonne National Laboratory and Northwestern University. PCx has nothing to do with the .pcx file format; it cannot be used to open files in this format. The current release is . Numerous small changes have been made since the last major release on ; see the change log for details. Version 1.1 contains no new algorithmic features; it differs from version 1.0 in that it provides hooks in the code that enable alternative linear solvers to be provided by the user. PCx is designed as a stand-alone solver. Because of its modular structure and fairly transparent data structures, it is not too difficult to integrate into your application.Together with some of our users, we have recently investigated new features such as a callable library and a MATLAB interface. Users who are interested in contributing other enhancements to PCx are encouraged to contact the authors Downloading and Installing PCx PCx is freely available, but is not public domain software. Commercial users should obtain a license.

15. Linear Programming FAQ sci.opresearch sci.answers news.answers Subject linear programming FAQ Followup-To sci.op-research Date 1 http://www.cis.ohio-state.edu/hypertext/faq/usenet/linear-programming-faq/faq.ht

Linear Programming FAQ From: 4er@iems.nwu.edu (Robert Fourer) Newsgroups: sci.op-research sci.answers news.answers Subject: Linear Programming FAQ Followup-To: sci.op-research 63gc0q$8lu@news.acns.nwu.edu 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 Plain-text version: ftp://rtfm.mit.edu/pub/usenet/sci.answers/linear-programming-faq 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 (

16. Linear Programming FAQ linear programming FAQ. From 4er@iems.nwu.edu (Robert Fourer 1, 1997* Q1. What is linear programming? * Q2. Where is there good http://isc.faqs.org/faqs/linear-programming-faq/

Linear Programming FAQ From: 4er@iems.nwu.edu (Robert Fourer) Newsgroups: sci.op-research sci.answers news.answers Subject: Linear Programming FAQ Followup-To: sci.op-research 63gc0q$8lu@news.acns.nwu.edu 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 Plain-text version: ftp://rtfm.mit.edu/pub/usenet/sci.answers/linear-programming-faq 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 (

17. NEOS Guide - Linear Programming BPMPD linear programming. CPLEX - linear and integer programming. C-WHIZ - linear programming models. Excel and Quattro Pro Solvers - spreadsheet-based linear, integer and nonlinear programming. http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Categories/linearprog.html

Linear Programming Solvers BPMPD - linear programming. CPLEX - linear and integer programming. C-WHIZ - linear programming models. Excel and Quattro Pro Solvers - spreadsheet-based linear, integer and nonlinear programming. FortMP - linear and mixed integer quadratic programming. GAUSS - matrix programming language. HS/LP Linear Optimizer - linear programming with OMNI language. KORBX - linear programming. LAMPS - linear and mixed-integer programming. LINDO Callable Library - linear, mixed-integer and quadratic programming. LINGO - linear, integer, nonlinear programming with modeling language. LOQO - Linear programming, unconstrained and constrained nonlinear optimization. LP88 and BLP88 - linear programming. MINOS - linear programming and nonlinear optimization. MOSEK - linear programming and convex optimization. MPSIII - linear and mixed integer programming (includes OML, WHIZARD, and DATAFORM). OML - linear and mixed-integer programming. OSL - linear, quadratic and mixed-integer programming. PCx - linear programming with a primal-dual interior-point method.

18. Linear Programming FAQ linear programming Frequently Asked Questions List Posted monthly to Usenet newsgroup sci.op-research World Wide Web version http// www. gov/ home/ otc/ Guide/ faq/ linear- programming- faq. Plain-text version ftp// rtfm. http://rutcor.rutgers.edu/~mnk/lp-faq.html

Linear Programming - Frequently Asked Questions List 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 Plain-text version: ftp://rtfm.mit.edu/pub/usenet/sci.answers/linear-programming-faq Date of this version: April 1, 1997 Q1. " What is Linear Programming ?" Q2. " Where is there a good code to solve LP problems?" Q3. "Oh, and we also want to solve it as an integer program ." Q4. "I wrote an optimization code. Where are some test models ?" Q5. "What is MPS format ?" Topics briefly covered: : "What is a modeling language?" : "How do I diagnose an infeasible LP model?" : "I want to know the specific constraints that contradict each other." : "I just want to know whether or not a feasible solution *exists*." : "I have an LP, except it's got several objective functions." : "I have an LP that has large almost-independent matrix blocks that are linked by a few constraints. Can I take advantage of this?" : "I am looking for an algorithm to compute the convex hull of a finite number of points in n-dimensional space."

19. Linear Programming Software for linear programming (including network linear programming) consumes morecomputer cycles than software for all other kinds of optimization problems http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/linearprog/

Software for linear programming (including network linear programming) consumes more computer cycles than software for all other kinds of optimization problems combined. There is a proliferation of linear programming software with widely varying capabilities and user interfaces. The most recent survey of linear programming software for desktop computers carried out by OR/MS Today (19 (1992), pp. 44-59) gave details on 49 packages! The basic problem of linear programming is to minimize a linear objective function of continuous real variables, subject to linear constraints. For purposes of describing and analyzing algorithms, the problem is often stated in the standard form where is the vector of unknowns, is the cost vector, and is the constraint matrix. The feasible region described by the constraints is a polytope, or simplex , and at least one member of the solution set lies at a vertex of this polytope. The simplex algorithm , so named because of the geometry of the feasible set, underlies the vast majority of available software packages for linear programming. However, this situation may change in the future, as more software for interior-point algorithms becomes available.

20. Topics In Linear Algebra An approach unifying the notions of system of equations, matrix inversion, and linear programming. http://ubmail.ubalt.edu/~harsham/opre640a/partXII.htm

Unification of System of Linear Equations, Matrix Inversion, and Linear Programming URL for this site is: http://ubmail.ubalt.edu/~harsham/opre640a/partXII.htm This site extends the existing one-way connections among the solving linear systems of equations, matrix inversion, and linear programming. The additional linkages empower the user to understand the wholeness and manifoldness of these topics. They also assist the user to model and solve a problem modeled as any one of the above topics by having access to a computer package solver. The goals are theoretical unification as well as advancements in applications. Illustrative numerical examples are presented. Professor Hossein Arsham To search the site , try E F ind in page [Ctrl + f]. Enter a word or phrase in the dialogue box, e.g. " inverse" or " equations" If the first appearance of the word/phrase is not what you are looking for, try F ind Next MENU Introduction LP Problem Solved by System of Equation Solver System of Equations Solution by LP Solver Solving for the Inverse of a Matrix Using LP Solver ... References and Further Readings Companion site I: Deterministic Modeling: Linear Optimization Companion site II: Decision Making Resources Companion site III: Operations Research (Index) Companion site IV: A Collection of JavaScript Applets-assisted E-labs Learning Objects Introduction Linear programming (LP), Linear systems of equations, and Matrix inversion are often favorite topics for both instructors and students. The ability to solve these problems by Gauss-Jordan pivoting (GJP), the widespread availability of software packages, and their wide range of applications make these topics accessible even for students with relatively weak mathematical backgrounds. The typical textbooks on LP usually devote separate sections for each topic. However, the relationships among these closely related topics are often not presented or thoroughly discussed. This article extends the existing one-way connections among these topics to construct a comprehensive two-way relationship as in the following figure. For each topic, it is shown how the problem may be modeled and solved by either of the associated methodologies.

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