R.J. Vanderbei. AMPL models. http://www.sor.princeton.edu/rvdb/ampl/nlmodels/.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1999 (Revision) This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W 31 109 Eng 38. Contents 1 Introduction 1 2 Largest Small Polygon (Gay [8]) 3 3 Distribution of Electrons on a Sphere (Vanderbei [13] 5 4 Sawpath Tracking (Vanderbei [13] 7 5 Hanging Chain (H. Mittelmann, private communication) 10 6 Shape Optimization of a Cam (Anitescu and Serban [1] 12 7 Isometrization of ff pinene (MINPACK 2 test problems [3] 15 8 Marine ....

....our C implementations, including the data structures used for each of problem. Implementations in AMPL and in C, along with sample drivers that use the C implementation with SNOPT, are available for downloading from our web site, http: www.mcs.anl.gov more cops. 2 2 Largest Small Polygon (Gay [8]) Find the polygon of maximal area, among polygons with n v sides and diameter d 1. Formulation The merit function is f(r; Gamma 1 2 nv Gamma1 X i=1 r i 1 r i sin( i 1 Gamma i ) r nv = 0; nv = and the constraints are r 2 i r 2 j Gamma 2r i r j cos( i Gamma j ) ....

D. Gay, AMPL models. http://www.netlib.org/ampl/models/.

.... of Mathematics, North Carolina State University, Raleigh, North Carolina 27695 (dmbortz unity,ncsu.edu) x Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (more mcs.anl.gov) Contents Abstract 1 1 Introduction 1 2 Largest Small Polygon (Gay [8]) 3 3 Distribution of Electrons on a Sphere (Vanderbei [13] 5 4 Sawpath Tracking (Vanderbei [13] 7 5 Hanging Chain (H. Mittelmann, private communication) 10 6 Shape Optimization of a Cam (Anitescu and Serban [1] 12 7 Isometrization of ff pinene (MINPACK 2 test problems [3] 15 8 Marine ....

....1 Introduction COPS is a collection of large scale nonlinearly Constrained Optimization ProblemS. We drew these test problems from a variety of sources, including some of the existing collections, such as the AMPL problems of Vanderbei [ the NETLIB collection of AMPL problems maintained by Gay [8]; the optimal control problems of Betts, Eldersveld, and Huffman [4] and the MINPACK 2 collection [3] We chose problems that arise in applications (for example, fluid dynamics, optimal shape design, population dynamics) or that have interesting features. The aim of COPS is to challenge and test ....

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D. Gay, AMPL models. http://www.netlib.org/ampl/models/.

....iteration. Thus for nonconvex problems, dual orderings appear to be essential, and are the default in LOQO. As a final note of caution, however, on convex problems it is possible that a primal ordering can produce far greater sparsity, depending on H and A. On the problem structure socp ([12]) LOQO solved with the primal ordering INTERIOR POINT METHODS FOR NONCONVEX NONLINEAR PROGRAMMING 7 in 2 minutes 20 seconds, and in 96 minutes with the dual ordering. Thus the ordering should be chosen with care, but if the problem is nonconvex, the dual always seems preferable. 3. HIGHER ....

....is 2787 whereas with it on the total number is 2404. While individual problems can vary significantly, overall the predictor corrector method seems to do very well. In addition to the Hock and Schittkowski test sets, we compared the two algorithms on three models from the second author s website [12] and 15 models from the CUTE [3] library of test problems. Some of these problems are larger (and therefore more interesting) As the problems get more difficult, the benefits of using the predictor corrector method become more apparent. The results are contained in the table 2. While this work is ....

R.J. Vanderbei. AMPL models. http://www.sor.princeton.edu/rvdb/ampl/nlmodels/.

....IPM S FOR NLP: FILTER METHODS AND MERIT FUNCTIONS 11 a test suite of 889 AMPL models, which form the test set for this paper. These models vary greatly in size and di#culty and have proved useful in drawing meaningful conclusions. All of the AMPL models used in our testing are available at [9]. The CUTE suite contains some problems that are excluded from our set. We have not yet converted to AMPL any models requiring special functions as well as some of the more complex models. We will continue to convert the remainder of the suite to AMPL models as time allows, but believe that the ....

R.J. Vanderbei. AMPL models. www.sor.princeton.edu/rvdb/ampl/nlmodels.

....C i j X i j subject to # i j A (k) i j X i j = b k , k = 1, 2, m X # 0. 24) We ve made four data sets: a small problem suggested by Masakazu Muramatsu, a max cut problem, and two max min eigenvalue problems. The data for these four problems can be downloaded from our web site [14]. Without setting parameter sdp to true, the nonlinear functions in kth diag go negative and the algorithm fails on all four problems. However, with the parameter set to true, LOQO correctly each of these four problems. 6.1. Exploiting Sparsity. The dual problem for (24) is maximize # k b k y k ....

R.J. Vanderbei. AMPL models. http://www.sor.princeton.edu/rvdb/ampl/nlmodels/.

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