Guide for Solving Optimization Problems
NAG, a not-for-profit numerical software development organization, devotes significant R&D resources to continually advance methods for solving optimization problems and similar computational challenges. The NAG Decision Trees are part of the documentation for one of the most rigorously tested and documented sets of optimization routines and other mathematical and statistical algorithms in the world, collected into the Numerical Algorithms Group Library. The NAG Library of routines, including the optimization chapters, can be called from diverse environments such as C++, Fortran, MATLAB and R.
Many of those who use NAGs routines, as the building blocks of their applications, rely on the knowledge base in NAGs exhaustive documentation as a part of the future-proofing of their application development investments. The Decision Trees, which are a feature of this documentation, are especially useful in helping both new and experienced users to select the appropriate routine for the problem at hand in a matter of minutes.
Dr. David Sayers, a Principal Technical Consultant at NAG commenting on the complexities of selecting optimization algorithms says, For maximum efficiency, different algorithms should be used for a different problem types. Often these types are characterized by the type of objective function that is to be minimized or maximized and by the types of constraints that are to be applied. Objective functions might be linear, quadratic (positive-definite or indefinite) or nonlinear. They may have a special form, like a sum of squares. They may be sparse or dense and they may be smooth or discontinuous. Combine these with the options for constraints: none, simple bound, linear or genuine nonlinear and we can see that a comprehensive chapter of optimization routines can be very large. To help the user to choose the right routine decision trees are invaluable.
With origins in several UK universities, the Numerical Algorithms Group (NAG), has its headquarters in Oxford, and is a not-for-profit organization that collaborates with world-leading researchers and practitioners in academia and industry. NAG serves its customers from offices in Oxford, Manchester, Chicago, Tokyo and Taipei, through field sales staff in France and Germany, as well as via a global network of distributors.
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