INSIDE THIS ISSUE
In our continuing efforts to supply our clients with the best software at affordable prices, WTI is pleased to announce the addition of Linear Programming (LP) and Quadratic Programming (QP) software to our offerings. The selection of the BPMPD package as the basis for our offerings stems from several considerations. The WTI product is called LP_QP_Solve. The author of BPMPD is Csaba Meszaros* of the Hungarian Academy of Sciences, Budapest Hungary. Below are the algorithmic highlights of this software.
Sparse Technology: This means that very large problems are accessible.
Interior Point Method: Problems can be solved very quickly and efficiently. The Interior point method is theoretically a polynomial time algorithm, but in practice, it is even more efficient than the current theory suggests.
Primal-Dual Method: Produces both primal and dual solutions simultaneously.
Robust: This is a very reliable code. It has proved to be especially effective on degenerate problems and infeasible problems, which is especially useful in debugging large models.
LP_QP_SOLVE solves the standard LP problem:
Min ctx
Subject to: a
LP_QP_SOLVE can solve the standard QP problem:
Min ctx + xtQx
Subject to: a
where Q is positive semi-definite. In both the LP and QP problems c, x, d, e are all vectors in Rn. The vectors a, b are in Rm. The matrices Q and A are n by n and m by n respectively.
Typical LP and QP application areas:
Finance: Portfolio Optimization (Modern Portfolio Theory (MPT), the Capital Asset Pricing Model (CAPM), and efficient frontier calculations) and multi-period investment problems.
Engineering: Electrical power flows through grids, solution of over-determined linear systems of equations, constrained curve and surface fitting.
OR: Optimal allocation of resources, scheduling production and inventory, resource planning.
LP_QP_SOLVE will be offered as a DLL. LP_QP_SOLVE is implemented in C and available as a function. The MPS file format is supported for LP problems and the QPS file format is supported for QP problems. Run-time and source code licenses are available. We understand that models can be large and difficult to maintain. WTI will also be available for consulting and modeling support.
LP_QP_Solve documentation is available on our web site (
web.wt.net/~wti/lp_qp_solve)We are now using html for the documentation of all our products.
A large body of test problems is available for LP codes. The largest repository of these tests can be found in the Netlib test suite. BPMPD has been extensively benchmarked and in fact has solved all the Netlib problems. The page ftp://plato.la.asu.edu/pub/lpbench.txt by Hans Mittelmann of Arizona State University contains some of the benchmarking information. This set of benchmarks clearly places BPMPD in the forefront of Interior Point Methods (IPMs) for solving LPs and QPs. To obtain research papers concerning the BPMPD algorithm, go to the web site ftp://ftp.sztaki.hu/pub/oplab/PAPERS
*Csaba Meszaros is affiliated with the Computer and Automation Research at the Hungarian Academy of Sciences, Budapest, Hungary.
IDL is the well-known and widely used product of Research Systems, Boulder, Colorado. It is a complete computing environment for the interactive analysis and visualization of data. IDL 5.1, the most recent version of IDL, has a new routine named CONSTRAINED_MIN for the solution of constrained nonlinear optimization problems that uses GRG2 as its solution engine. The CONSTRAINED_MIN interface makes it possible to solve constrained optimization problems in the IDL environment. The objective function and constraint functions are supplied to CONSTRAINED_MIN as an IDL function. For more information about IDL and CONSTRAINED_MIN you can contact RSI by phone: 303-786-9900, by email:
info@rsinc.com, or visit their web site: www.rsinc.com.EMPV Program Developed By WTI
Windward Technologies has developed EMPV (Effective Management of Process Variability) exclusively for Francis Pitard Sampling Consultants (FPSC). The EMPV program is easy-to-use and learn, powerful, and fully-integrated. It features advanced chronostatistics functions that facilitate the generation of variograms, control charts, moving average charts, and pie charts. The program is written in Visual Basic to operate in the Windows 95 environment. It uses two Active X controls from Visual Components, Formula One and First Impression. Formula One provides an Excel compatible workbook interface that EMPV uses for its input data. First Impression is a graphics control that generates charts, such as variograms, for EMPV. First Impression provides a host of runtime features that make it possible for EMPV users to customize charts. For more information about Formula One and First Impression, visit the Visual Components web site:
www.visualcomp.com.Francis Pitard is a recognized international expert in all aspects of Total Quality Management, Sampling, Statistical Process Control, and the practical application of statistical methods for problem solving. For more information about Francis Pitard and EMPV you can contact FPSC by phone: 303-451-7893, by email:
info@fpscsampling.com, or visit their web site: www.fpscsampling.com.
What’s New at WTI
WTI
or its products can be found at the following Internet Web sites:Research Systems Inc. (CONSTRAINED_MIN / GRG2) www.rsinc.com
Visual Solutions (VisSim/OptimizePRO)
www.vissim.com, click on Partners.Mathworks (GRG2, BCLS, and RBFpack)
Free Copy of Curvi Available
Curvi is a program that solves nonlinear optimization problems of the following form:
Minimize or maximize f (X),
subject to xlbj
£ xj £ xubj for j=1,...,n.X is a vector of n variables, x1 ,...,xn, and the function f depends on X.
Curvi uses first and second partial derivatives of the objective function f with respect to each variable xj. These derivatives are computed automatically by finite difference approximations (either forward or central differences) unless the user supplies a function that evaluates them using formulas or other methods.
Curvi is a set of three solvers: curvif, curvig, and curvih. Curvif requires only function values. Curvig requires function values and gradient values, and curvih requires Hessian values also. Performance is improved when gradient values or gradient and Hessian values are supplied, but when this is not possible, curvif will do a good job of computing these values numerically.
Curvi is available as a DLL and in Fortran source code formats. The DLL version is designed for the Windows 95 operating system. C programs (MS Visual C++) can use the DLL, as can Fortran programs (Digital Visual Fortran), as well as any Windows application capable of referencing a DLL.
The algorithm for unconstrained optimization used by Curvi is described in: A Curvilinear Search using Tridiagonal Secant Updates for Unconstrained Optimization, by J.E. Dennis, N. Echebest, M.T. Guardarucci, J.M. Martinez, H.D. Scolnik and C. Vacchino., in SIAM J. on Optimization, Vol.1, Number 3, August 1991, page 351.
Curvi is a robust code capable of solving very difficult optimization problems. The example shown on our Web site challenges many existing optimization codes. Try it on your favorite code and compare with the performance of Curvi. You can download the DLL version of Curvi for a 90-day free trial, and for a limited time, WTI is offering a free license for Curvi to anyone requesting it. The web address is
web.wt.net/~wti.You will need to request a password from WTI in order to install the software.
Presentations and Publications
Phil Smith
has been invited to be on the Mathematical Sciences Advisory Committee of Purdue University."Using Matlab and RBFpack" was the title of the talk Phil gave at the Texas A&M Spring Approximation Meeting. The talk highlighted the usage of Matlab graphics and the Matlab RBFpack connection.
Tom Aird attended the Spring meeting of the Dean’s Advisory Council, School of Science, Purdue University, in West Lafayette, Indiana, May 8-10. Tom gave a talk, "ConFit: Shape Preserving Curve Fitting", to the Computer Sciences Department on May 7.
ConFit Available on Web Site
The constrained curve-fitting program ConFit, discussed in our Q1 98 newsletter, is available on our web site. This flexible, easy to use program allows you to produce curve fits to data that have special characteristics such as monotonicity or convexity. We call this shape preservation. The program is spreadsheet based with an extremely easy user interface. Plots of the data and the approximating function can be produced with the click of a button. You can download this program for a 90-day free trial. The web address is
web.wt.net/~wti/confit. You will need to request a password from WTI in order to install the software.
Consulting and Program Development Services We offer services in the following areas: Parallel computing, MPI, DSP, C, C++, Visual Basic, Fortran, Assembler, Applied Math, Visualization, Optimization, and Training. If your organization would benefit by having access to a part-time mathematical software development team, contact us!
GUARANTEE We are so convinced in the quality of this service and our products in general that if you are not completely satisfied, we offer a 90 day money-back guarantee.
This is a quarterly newsletter of Windward Technologies, Inc. Please let us know what your interests are and what sort of articles you would like to see. Please contact us if you would like to have your name added to our newsletter mailing list or if you would like to contribute an article to the newsletter
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Windward Technologies, Inc. |
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The Wind is a quarterly newsletter written and edited by Tom Aird and Phil Smith. Please let us know what your interests are and what type of articles you would like to see. If you would like to contribute an article to the newsletter, please contact us at
WTI@aol.com.
Regards,
Tom Aird
and
Phil Smith