41. IngMath Program can be used for study purposes by students and for mathematical calculations by engineers, natural scientists and mathematicians. It covers linear algebra, linear programming, transport optimization and rational functions. http://people.freenet.de/hebausch/ingmathe.html

Deutsche Version IngMath Software package Engineering Mathematics Short description Examples Prices Distribution ... Download Short description of IngMath IngMath (Engineering Mathematics) contains all essential numerical and other methods which are important for the mathematical education of students of technical and economical courses. The program is very easy to manage and may be used to carry out calculations, for mathematical experiments and for demonstrations in lectures and seminars. Contents: Linear algebra, linear programming, transport optimization, complex numbers and functions, real functions of one or many variables, differential equations (incl. systems), spline functions, systems of nonlinear equations or inequalities, nonlinear regression and others. Details Attention!! New version: Actualized at 15 February 2002. The shareware version is english, the full version exists in german and in english. Requirements: The operation system is DOS. Under WINDOWS 9x or Me one can use the program optimally. For a german CD-Rom version WINDOWS 9x or Me is needed.

42. Linear Programming linear programming. linear programming problems are intrinsically easier to solve than nonlinear problems. In an NLP there may be http://www.frontsys.com/algolpqp.htm

Linear Programming Linear programming problems are intrinsically easier to solve than nonlinear problems. In an NLP there may be more than one feasible region and the optimal solution might be found at any point within any such region. In contrast, an LP has at most one feasible region with "flat faces" (i.e. no curves) on its outer surface, and the optimal solution will always be found at a "corner point" on the surface where the constraints intersect. (In some problems there may be multiple optimal solutions, all of them lying along a line between corner points, with the same objective function value.) This means that an LP Solver needs to consider many fewer points than an NLP Solver, and it is always possible to determine (subject to the limitations of finite precision computer arithmetic) that an LP problem (i) has no feasible solution, (ii) has an unbounded objective, or (iii) has an optimal solution (either a single point or multiple equivalent points along a line). Problem Size and Numerical Stability Because of their structural simplicity, the main limitations on the size of LP problems which can be solved are time, memory, and the possibility of numerical "instabilities" which are the cumulative result of the small errors intrinsic to finite precision computer arithmetic. The larger the model, the more likely it is that numerical instabilities will be encountered in solving it.

43. Annotated Bibliography On Linear Programming Models ITORMS title. ANNOTATED BIBLIOGRAPHY ON linear programming MODELS. This bibliography consists of the early papers on linear programming model formulations. http://catt.bus.okstate.edu/itorms/volumes/vol1/papers/murphy/

ANNOTATED BIBLIOGRAPHY ON LINEAR PROGRAMMING MODELS Frederic H. Murphy Temple University Philadelphia PA Go to the Overview Go to the Bibliography OVERVIEW This bibliography consists of the early papers on linear programming model formulations. It includes some papers that are not about linear programming models but are relevant to understanding the early literature. Examples of these non-LP papers are the Markowitz portfolio model, some integer programming models and papers on input-output analysis. The summaries of the paper are mine and not abstracts, since many of the papers from this era did not have abstracts. I have not read the papers that do not have summaries because I was not able to get copies of them. The value of this bibliography resides in bringing together a literature that is still relevant for understanding LP modeling issues and modeling in general. By scanning the papers, one can see the evolution of issues and trends in the thinking of those involved in developing the field. Personal creativity in model formulation often follows the same pattern as historical creativity, that is, the first formulation of a new model, and this bibliography allows one to trace the historical roots of model formulation. See Murphy and Panchanadam (1995) for an example of how this bibliography can be used for current research.

44. Arageli C++ template library for computations in ARithmetics, Algebra, GEometry, Linear and Integer linear programming. Supports arbitrary length integers, rationals, vectors, matrices. http://www.uic.nnov.ru/~zny/arageli/arageli.html

Arageli Arageli is the C++ library and the package of programs for computations in ar ithmetic, a lgebra, ge ometry, l inear and i nteger linear programming. Current version contains the implementation of arbitary precision arithmetic on integer and rational numbers (synonyms: multiple precision arithmetic, multiple precision numbers, arbitrary precision arithmetic, arbitrary precision numbers, big numbers). Some time-critical parts are written in assembler. You can use this assembler code or C++ code instead. If you'd like to use the library you can: Read (incomplete) documentation for version 2.0 beta (online) Download Arageli library 2.0 beta (with documentation) Read documentation for version 1.1.1 (online) Download Arageli library 1.1.1 (with documentation) Download Arageli library 1.1 (with documentation) Download Arageli library 1.0 (with documentation) If you'd like to use the package you can: Read description of some programs (in Russian) Download the package If you are interested in Pascal library for arbitary precision arithmetic you can also try my old BP 7.0 unlimited-precision arithmetic package my home page File translated from T E X by T T H , version 3.00

45. Linear Programming linear programming. Michael Carter. Senior DANTZIG is the classic exposition of linear programming by its inventor, George Dantzig. He http://www.econ.canterbury.ac.nz/mike4.htm

UoC Info Econ Home Dept Info Staff ... Air Quality Linear Programming Michael Carter Senior Lecturer in Economics University of Canterbury Note: This essay was prepared for Reader’s Guide to the Social Sciences to be published by Fitzroy Dearborn Beasley, J. E.(editor), Advances in Linear and Integer Programming , Oxford: Clarendon Press, 1996. Carter, Michael, "Linear Programming with Mathematica" in Computational Economics and Finance , edited by Hal R. Varian, New York: Springer-Verlag, 1996 Chvátal, Vašek, Linear Programming , New York: Freeman, 1983 Dantzig, George B. Linear Programming and Extensions , Princeton NJ: Princeton University Press, 1963 Dantzig, George B. and Mukund N. Thapa, Linear Programming 1: Introduction , New York: Springer-Verlag, 1997 Dorfman, Robert, Paul A. Samuelson and Robert M. Solow, Linear Programming and Economic Analysi s, New York: McGraw-Hill, 1958 Garfinkel, Robert and George Nemhauser, Integer Programming , New York: Wiley, 1972 Nemhauser, G.L., A.H.G. Rinnooy Kan and M.J. Todd (editors), Optimization , Volume 1, Handbooks in Operations Research and Management Science, Amsterdam, London, New York and Tokyo: North-Holland, 1989 Roos, C., T. Terlaky and J.-Ph. Vial

46. Linear Programming Ratfor code for the primaldual log barrier form of the interior point LP solver of Lustig, Marsten and Shanno, ORSA J Opt 1992. http://www.econ.uiuc.edu/~roger/research/rqn/rqn.b

<'End of fnc.r' #Outer wrapper for the new rqn functioncalls a frisch-newton LP solver #Does preprocessing using the functions globit and checkit to reduce initial n subroutine rqm(n2,p,a,y,rhs,d,wn,wp,beta,eps,tau,s,aa,hist) integer n,p,s(n2),hist(3,32),kit,nit,mit,m,mm,n2,maxnit,maxmit,mlim double precision a(p,n2),y(n2),rhs(p),d(n2),wn(1),wp(p,p+3),aa(p,p) double precision beta,eps,tau,omega,sparsity #real ut,time,udt data zero/0.0d0/ data one/1.0d0/ data two/2.0d0/ maxmit=8 maxnit=4 n=n2-2 m=2*nint(n**(2./3.)) mlim = 5*m mit=0 kit=0 #outer loop on the initial sample size while(mit <=x <0)deltap=dmin1(deltap,-x(i)/dx(i)) if(ds(i) <0)deltap=dmin1(deltap,-s(i)/ds(i)) if(dz(i) <0)deltad=dmin1(deltad,-z(i)/dz(i)) if(dw(i) <0)deltap=dmin1(deltap,-x(i)/dx(i)) else deltap=dmin1(deltap,-s(i)/ds(i)) if(dz(i) <0)deltad=dmin1(deltad,-z(i)/dz(i)) if(dw(i) <'End of sparsity.r' #This is a Siddiqui sparsity function estimate based on residuals double precision function sparsity(n,u,tau) integer n,nd,enuf double precision u(n),tau,h,qhi,qlo,half data half/0.5d0/ data enuf/600/ #bandwidth: approximate Hall-Sheather method - quadratic approx max error 1% nd=nint((.05 + 3.65*tau - 3.65*tau**2)*(n**(2./3.))) h=dfloat(nd)/dfloat(n) #compute Siddiqui estimator call kuantile(n,u,tau+h,qhi,enuf,half,half) call kuantile(n,u,tau-h,qlo,enuf,half,half) sparsity=(qhi-qlo)/(h+h) return end #function to compute pth quantile of a sample of n observations subroutine kuantile(n,x,p,q,mmax,cs,cd) integer n,k,l,r,mmax double precision x(n),p,q,cs,cd if(p

47. MIT OpenCourseWare | Electrical Engineering And Computer Science | 6.252J Non-li 6.252J / 15.084J Nonlinear programming, Spring 2003. Textbook cover of Nonlinear programming 2nd Edition, by DP Bertsekas, Athena Scientific, 2000. http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-252JNon-

var wtl_loc = document.URL.indexOf('https:')==0?'https://a248.e.akamai.net/v/248/2120/1d/download.akamai.com/crs/lgsitewise.js':'http://crs.akamai.com/crs/lgsitewise.js'; document.write(""); Search All OpenCourseWare This Course Advanced search Course Home Syllabus Calendar ... Non-linear Programming, Spring 2003 6.252J / 15.084J Non-linear Programming, Spring 2003 Textbook cover of Nonlinear Programming: 2nd Edition , by D.P. Bertsekas, Athena Scientific, 2000. (Image courtesy of Dimitri Bertsekas and Athena Scientific.) Highlights of this Course This course features a full set of lecture notes , in addition to other materials used by students in the course. The materials are largely based on the textbook, Nonlinear Programming: 2nd Edition publisher's site for more information). Course Description 6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems.

48. EE236A: Linear Programming EE236A linear programming. PCx is a linear programming package developed at Argonne National Laboratory and Northwestern University. http://www.ee.ucla.edu/ee236a/ee236a.html

EE236A: Linear Programming UCLA Electrical Engineering Department Fall Quarter 2003-2004 Homework assignments and solutions Additional lecture notes Course information Software ... Course description Homework assignments and solutions Assignments Homework 1 (due 10/7): Exercises 1, 3, 4, 11 and two additional problems Homework 2 (due 10/14): Exercises 7, 12, 13, 15, 17 and an additional problem . Exercises 13 and 15 require an LP solver. The software section below lists several available solvers. Homework 3 (due 10/21): Exercises 16, 18, 19, 20, 21, 22. Homework 4 (due 10/28): Exercises 24, 25, 26, 27, 40, 41. Homework 5 (due 11/4): Exercises 33, 34, 35, 39, and two additional problems Homework 6 (due Thursday 11/13): Exercises 36, 37, 38, 42, 48, 49. Homework 7 (due 11/20): Exercises 53, 54, 55, 56, 57. Homework 8 (due 12/4): Exercise 65. Submit your code by email to vandenbe@ee.ucla.edu. The exercise numbers refer to the collection of problems at the end of the lecture notes.. The following matlab files are needed for some of the problems: ex10data.m

49. Springer-Verlag - Foundations Of Computing One of the wellknown early textbooks, by Herbert Edelsbrunner. Includes chapters on arrangements, convex hulls, linear programming, planar point location, Voronoi diagrams, and separation and intersection. http://www.springer.de/cgi-bin/search_book.pl?isbn=3-540-13722-X

50. Robust Linear Programming And Optimal Control TITLE Robust linear programming and optimal control; AUTHORS L. Vandenberghe, S. Boyd. M. Nouralishahi. ABSTRACT We describe an http://www.ee.ucla.edu/~vandenbe/robustlp.html

TITLE: Robust linear programming and optimal control AUTHORS: L. Vandenberghe S. Boyd . M. Nouralishahi ABSTRACT: We describe an efficient method for solving an optimal control problem that arises in robust model-predictive control. The problem is to design the input sequence that minimizes the peak tracking error between the ouput of a linear dynamical system and a desired target output, subject to inequality constraints on the inputs. The system is uncertain, with an impulse response that can take arbitrary values in a given polyhedral set. The method is based on Mehrotra's interior-point method for linear programming, and takes advantage of the problem structure to achieve a complexity that grows linearly with the control horizon, and increases as a cubic polynomial as a function of the system order, the number of inputs, and the number of uncertainty parameters. STATUS: Proceedings of the 15th IFAC World Congress on Automatic Control, July 2002. CONFERENCE PAPER: postscript pdf FULL PAPER: postscript pdf

51. Linear Programming - Simplex Method linear programming Simplex Applet. By Pedro Miguel Silva and Tiago Castro Guise Version 1.0 - Lisbon, July 1998, updated on October 1999 linear programming http://algos.inesc.pt/lp/

Linear Programming - Simplex Applet By Pedro Miguel Silva and Tiago Castro Guise Version 1.0 - Lisbon, July 1998, updated on October 1999 You are visitor number to this page since last reboot. Simplex Applet: The available LP algorithms are: Simplex Method, Revised Method, Primal Dual and Simplex Dual. Enter Your Linear Program: ... Applet Controls here, if you had java in your browser. How the Applet Works: Buttons: Solve - Solve your linear program. Abort Abort the execution of the algorithm. Clear - Allows you to clear fields. About - Brings up an about window. Choice Menus: First Choice Menu - With this options you can chose clear the field results or clear the field linear program. It is also, available the options of no clear fields and clear all fields. Second Choice Menu - Chose the algorithm you want Simplex, Revised Simplex, Primal Dual or Simplex Dual. . Third Choice Menu - Chose output options. Linear Programming: A linear program is a problem a problem that can be expressed as follows: min cx (Standard Form) subject to Ax = b x >= Where "x" is the vector of variables to be solved, "A" is the matrix of known coefficients and "c" and "b" are vectors of known coefficients. The Expression "cx" is called the objective function and the equations "Ax = b" are called the constraints.

52. Welcome To Easyworm's Site! linear programming software for Windows 9x/NT/2000. http://www.easyworm.com/

53. Linear Programming - Wikipedia, The Free Encyclopedia linear programming. From Wikipedia, the free encyclopedia. Many practical problems in operations research can be expressed as linear programming problems. http://en.wikipedia.org/wiki/Linear_programming

Linear programming From Wikipedia, the free encyclopedia. Linear programming (LP for short) is the process of solving a system of linear equalities and linear inequalities over a set of unknown real variables, along with a linear objective function to be maximized. Many practical problems in operations research can be expressed as linear programming problems. For instance, if x is the number of acres planted with wheat and x is the number planted with corn, and a farmer has a limited number of acres A , and has a limited permissible amount F of fertilizer and P of insecticide which can be used, each of which is required in different amounts per acre ( F F P P ) for wheat and corn respectively, and knows the selling price of wheat S and the selling price of corn S , then the optimal number of acres to plant with wheat vs corn can be expressed as a linear program: Subject to the linear constraints: x x x x A (limit on total acrage) F x F x F (limit on fertilizer) P x P x P (limit on insecticide) maximize the objective function: S x S x Due to the geometry of these kinds of linear constraints and the linear objective function, LP problems are "convex", which means that there are no local optima (aside from the global optimum). Furthermore, in LP the solution must be at a vertex of the n-dimensional

54. Linear Programming FAQ FAQ Non.com FAQ Mirrors. Prev lilafeng-faq Next literate-programming-faq linear programming FAQ. Q1. What is linear programming? . http://www.non.com/news.answers/linear-programming-faq.html

Non.com FAQ Mirrors Prev: lila-feng-faq Next: literate-programming-faq Linear Programming FAQ [ ] [ ] 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 Q1. "What is Linear Programming?" Q2. "Where is there good software to solve LP problems?" 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 (

55. Stanford Business Software Sells Fortran 77 optimization codes MINOS (linear programming and nonlinear optimization), SNOPT (largescale quadratic and nonlinear programming), NPSOL (nonlinear programming), LSSOL (Linearly constrained linear least squares problems and convex quadratic programmmin), and QPOPT (linear and quadratic programming). http://www.sbsi-sol-optimize.com/

Welcome to Stanford Business Software's site for distribution of SOL/UCSD Optimization Software;a suite of packages for solving linear, quadratic, and nonlinear programs. The algorithms and software are produced by researchers Walter Murray and Michael Saunders at the Systems Optimization Laboratory (SOL) , Stanford University, and researcher Philip Gill at the Department of Mathematics, UC San Diego.

56. The Diet Problem The Diet Problem An Application of linear programming. The recent change more interesting facts. Formulation of problem as linear program. http://www-fp.mcs.anl.gov/otc/Guide/CaseStudies/diet/

The Diet Problem: An Application of Linear Programming The recent change of web server at Argonne and the loss of some of the source code for this Case Study has rendered it inoperable. We are currently trying to fix it. We apologize for any inconvenience. CLICK HERE for the demo! Or try the following version without tables What's New Edit the Constraints! Helpful Suggestions for Infeasible Diets!! Description of the diet problem The goal of the diet problem is to find the cheapest combination of foods that will satisfy all the daily nutritional requirements of a person. The problem is formulated as a linear program where the objective is to minimize cost and meet constraints which require that nutritional needs be satisfied. We include constraints that regulate the number of calories and amounts of vitamins, minerals, fats, sodium and cholesterol in the diet. The mathematical formulation is simple, but you will find out by running the model that people do not actually choose their menus by solving this model. Our nutritional requirements can be met yet our concerns for taste and variety go unheeded. We would never drink gallons of vinegar nor include a few boullion cubes in our meals; however, such "optimal" menus have been created using this model. Read more about the history of the diet problem for more interesting facts.

57. Linear Programming Software for linear programming (including network linear programming) consumes more computer 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.

58. Eudoxus Systems Using optimization to solve business problems. Includes lecture notes and case studies on the practical application of linear programming and optimization. http://www.eudoxus.com

Home Search About us Tools We Use What is Optimization? ... Site Map Home Thank you for visiting Eudoxus Systems' web site. Eudoxus Systems develops computer-based solutions to hard business problems by applying advanced mathematical techniques based on optimization , also known as Mathematical Programming (MP). You can find more information about our products and services and the tools we use on this site or you can contact us by telephone or fax. We regret that the prevalence of viruses and spam has caused us to remove our email address from this site. This site also contains lecture notes about how to use optimization and an archive of newsletters about optimization techniques and applications. These show how we and others have used optimization to improve business operations around the world. All of this material can be downloaded for use with Acrobat reader and can be reproduced for non-commercial purposes without fee. We hope that this site is of use to students. We ask them, however, to understand that we are a business and that we have to earn all our revenue. Please can students not contact us for further information or to seek internships. If you have difficulty reading text on this site you can resize it as follows: click on View in your browser click on Text Size select the appropriate text size.

59. Relationship To Linear Programming Relationship to linear programming. there is an associated linear program called the linear relaxation formed by dropping the integrality restrictions http://mat.gsia.cmu.edu/orclass/integer/node12.html

Next: Branch and Bound Up: Solving Integer Programs Previous: Solving Integer Programs Relationship to Linear Programming Given an integer program there is an associated linear program called the linear relaxation formed by dropping the integrality restrictions: Since (LR) is less constrained than (IP), the following are immediate: If the objective function coefficients are integer, then for minimization, the optimal objective for (IP) is greater than or equal to the ``round up'' of the optimal objective for (LR). For maximization, the optimal objective for (IP) is less than or equal to the ``round down'' of the optimal objective for (LR). So solving (LR) does give some information: it gives a bound on the optimal value, and, if we are lucky, may give the optimal solution to IP. We saw, however, that rounding the solution of LR will not in general give the optimal solution of (IP). In fact, for some problems it is difficult to round and even get a feasible solution. Michael A. Trick Sun Jun 14 12:49:07 EDT 1998

60. MATLAB OPTIMIZATION - TOMLAB commercial Provides stateof-the-art optimization, with fast and robust solutions to sparse and dense linear, quadratic and nonlinear programming problems. http://tomlab.biz/

Your browser doesn't support JavaScript 1.2. LOGIN REGISTER myTOMLAB LATEST NEWS ... Online documentation released for all solver options. May 21th 2004 TOMLAB Quickguide availble for all problem types. Download from the manuals page May 18th 2004 TOMLAB /OQNLP v2.0 released. Many general improvements to the multi-start features. Read more >> Apr 28th 2004 TOMLAB /PATH now released. Linear and nonlinear mixed complementarity problems can now be solved with TOMLAB. Read more >> Apr 17th 2004 TOMLAB Base Module and TOMLAB /CPLEX additions. Download TOMLAB v4.3 Read more >> Mar 25th 2004 TOMLAB released for MAC OS X users. Download TOMLAB v4.2.1 Read more >> Mar 22nd 2004 TOMLAB /CGO v2.0 released. Costly integer problems now handled. Download TOMLAB v4.2.1 Read more >> Mar 8th 2004 Tomlab announces a cooperation with LINDO Systems, Inc. . TOMLAB /LINDO to be released. Read more >> Mar 7th 2004 TOMLAB /MAD released. A package for MATLAB Automatic Differentiation. Read more >> News archive >> PARTNERS PEN OPT The TOMLAB Optimization Environment is a powerful optimization platform for solving applied optimization problems in Matlab. TOMLAB provides a wide range of features, tools and services for your solution process. Read more about Tomlab >> The leading optimal control tool is now available: TOMLAB /DIDO Purchase TOMLAB online >> Are you looking for a solver to embed in your system?

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