Gay, D.M., "Electronic mail distribution of linear programming test problems", COAL Newsletter, Mathematical Programming Society, 13, 1985, p. 10--12.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in shorter time especially for harder problems. Our implementation is rather experimental, we have used an unsophisticated B B algorithm. As a consequence, it is rather slow and we could not solve all the problems in MIPLIB3. Models of the second set of test problems are from netlib lp data [1]. To make them MILP problems a subset of the variables have been changed to integer variables in each selected problem. The problems statistics are shown in Table 3. Looking at the results in Table 4 we can say that GA is roughly more than twice as fast as DF for most of the models. 5 Conclusion, ....

Gay, D.M., "Electronic mail distribution of linear programming test problems", COAL Newsletter, Mathematical Programming Society, Vol. 13, 1985, pp. 10--12.

....package to the reduced matrix K r . Similarly for least squares problems if many rows of the observation matrix have special structure. 7 Numerical Results To illustrate some e#ects, we report results from running the barrier code PDQ1 on two eminent LP problems from the Netlib collection [9]. The problems were scaled and then regularized (#, # 0) We requested 6 digits of accuracy in the regularized solution (x, #) Iteration counts are about 10 greater when 8 digits are required. Times are CPU seconds on a DEC Alpha 3000 400 workstation with about 16 digits of precision. MA47 ....

D. M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, 13 (1985), pp. 10--12.

....by the particular solver or optimization engine. In general, long term strategies should include a mathematical programming standard scalar format, which allows automorphic translation to and from this format. This has been accomplished for linear model with the long accepted standard MPS format [9] and recently work focused on a broader set of models has been done by introducing a format based on XML [13] 3.2 Data Collection Tools Reproducible data production and collection requires an automated system that provides information about the testing environment (version of software, ....

Gay, D. M.: Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society COAL Newsletter (1985)

....is not activated (Figure 22) and when it is (Figure 23) The number of nonzero entries in L falls from 11933 to 7896, a 33.8 reduction. Tables I and II illustrate applying SPARSE on a set of linear programming test problems that includes several linear programs publicly available through NETLIB. [12] Figure 23. Nonzero pattern of LU factors after SPARSE nonz(L) 7896. TABLE I Density Reduction Problem nonz(A) nonz(s(A) Reduction nonz(L) nonz(s(L) Reduction Afiro 102 102 0.00 107 107 0.00 AdLittle 417 393 5.76 404 383 5.20 Scagr7 457 434 5.03 734 731 0.41 Sc205 663 661 0.30 1182 ....

....of the selected row permutation. Consequently, we face prohibitively high computational effort and storage requirements in the Gaussian elimination procedure. We illustrate this situation with Problem Israel from the collection of linear programming test prob lems available through NETL1B. [12] From the nonzero pattern of the linear programming coefficient matrix presented in Figure 24, we detect the presence of a few dense columns. Figure 25 depicts the nonzero pattern for the AA r matrix, which is already very dense, in spite of the ordering procedure. Of course, the corresponding LU ....

D.M. Gay, 1985. Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society Committee on Algorithms Newsletter 13, 10-12.

....diagonal) and this holds also in the symmetric case. The matrices well1850, gemat1, impcol b, west0381, gemat11, bcsstk32, and bcsstk30 were obtained from the Rutherford Boeing collection [13, 14] the matrix memplus from the Matrix Market [8] dfl001 and cre b (part of the Netlib LP collection [19]) nug30, onetone2, lhr34, and finan512 were obtained from the University of Florida collection [12] hyp 200 2 1 is a matrix generated by the MLIB package [7] representing a five point Laplacian operator on a 200 200 grid with periodic boundaries. The matrix tbdmatlab is a term by document ....

D. M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, 13 (1985), pp. 10--12.

....and least squares (PCGLS) method [4] The termination criteria in PCGLS routine are when either the number of PCGLS iterations has reached a prescribed integer t or when kvk 2 10 Deltay Gamma AGh. 16 The test problems used in our experiments are all from the Netlib set of linear programs [8]. In Figures 1 and 2 below, we give some examples to demonstrate the effectiveness of the preconditioner for the weighted least squares problems. The results are generated from one of the Netlib test problem blend at a particular interior point iteration. 1.5 1 0.5 0 0.5 1 1.5 2 2.5 0 5 10 ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....of iterations allowed. This is set to 100 iterations. For the starting value we use the least squares solution [9, 14] x 0 = A T A) 1 A T y: In numerical experiments we set f = 10 3 and x = 10 3 , pcgls = 10 5 , 1, and = 0:1. We extract the matrix A from the netlib set [10] of linear programming problems. The true solution vector was taken to be a vector of all ones, and the right hand side was chosen to be y = Ax N(0; 1) except the outliers were obtained by adding 100 N(0; 1) to m 1 (m 1 is number of outliers) randomly chosen elements of b. The matrices H and G ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13(1985), pp.10-12.

....gradients and computing Cholesky factors. The construction of the preconditioner (updating of the triangular factors) can be done in parallel. 4 Numerical Results Here, we give some numerical results using the same implementation details as in [2] The test problems are from the Netlib set [5] of linear programs. The test code is implemented in MATLAB The variable ffl is a proximity measure of the interior point iterations to a solution of the linear programming problem and is the number of iterations (or corrections) allowed for the preconditioned conjugate gradient method. The ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....v k 1 = AGr k 1 s k 1 = Mv k 1 fl k 1 = s T k 1 v k 1 fi k = fl k 1 fl k p k 1 = s k 1 fi k p k k k 1 end fwhileg 5 Numerical results In this section we present some numerical results. Here, m and n are the number of rows and columns respectively, after preprocessing the problems [6]. We have implemented the Primal Dual Newton (PDN) and mixed primal dual Newton (mixed PDN) algorithms. Our implementation in this paper is done entirely in MATLAB 2 . We use a starting point (x 0 ; y 0 ; z 0 ) that is identical to the one given by Mehrotra [9] The termination criteria in ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....as many solves as for forming M . Forming M also involves forming and factorizing the q by q matrix F . Computing Mh requires 2 solves with a full right hand side, and approximately 4nnz( V ) 2q 2 m floating point operations. Numerical testing on the large Netlib test problems [7] shows that V is a sparse matrix and V is almost a dense m Theta q matrix. When using the Sherman Morrison Woodbury formula approach, Mh is computed using (2.10) Modification of the Triangular Factors We consider the case where a factorization of a symmetric positive definite matrix is ....

....ffl is large the maximum number of iterations in the iterative solver is a small value, and when ffl falls below a certain predefined constant the maximum number of iterations is increased in order to attain both primal and dual feasibility. Test problems from the Netlib set of linear programs [7] are used in the testing. The test code is implemented in MATLAB 1 . A direct step consist of computing AGA T and its Cholesky factor, and two solves with a full right hand side. An iterative step consist of forming M (for a given q) and the PCGLS iterations. We define the break even point for ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....A) Gamma1 A T y: In numerical experiments we set ffl f = 10 Gamma3 and ffl x = 10 Gamma3 , ffi pcgls = 10 Gamma5 , fi = 1, and oe = 0:1. The implementation is done in MATLAB 1 . Distribution of Eigenvalues of the Preconditioned Matrix We extract the matrix A from the netlib set [8] of linear programming problems. The true solution vector is taken to be x, the vector of all ones, and the right hand side was chosen to be y = Ax oeN(0; 1) except the outliers are obtained by adding 100oeN(0; 1) to m 1 (m 1 is number of outliers) randomly chosen elements of y. In our ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13(1985), pp.10-12.

....we set ffl f = 10 Gamma3 and ffl x = 10 Gamma3 . Furthermore, we set ffi pcgls = 10 Gamma5 , fi = 1, and oe = 0:1. The implementation is done in MATLAB 1 . 5 Numerical Experiments 5. 1 Distribution of Eigenvalues of Preconditioned Matrix We extract the matrix A from the netlib set [9] of linear programming problems. The true solution vector x is taken to be a vector of all ones, and the right hand side is chosen to be y = Ax oeN(0; 1) except the outliers are obtained by adding 100oeN(0; 1) to m 1 (m 1 is number of outliers) randomly chosen elements of y. In all experiments ....

Gay, D.M., Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....set to 100 iterations. For the starting value we use the least squares solution [8, 13] x 0 = A T A) Gamma1 A T y: In numerical experiments we set ffl f = 10 Gamma3 and ffl x = 10 Gamma3 , ffi pcgls = 10 Gamma5 , fi = 1, and oe = 0:1. We extract the matrix A from the netlib set [9] of linear programming problems. The true solution vector was taken to be a vector of all ones, and the right hand side was chosen to be y = Ax oeN(0; 1) except the outliers were obtained by adding 100oeN(0; 1) to m 1 (m 1 is number of outliers) randomly chosen elements of y. The matrices H and ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13(1985), pp.10-12.

....Having established the theoretical bounds, we need to compare with actual bounds on eigenvalues and distribution of eigenvalues of the preconditioned matrices based on real test problems. In this paper, we generate the test problems as follows: We extract the matrix A from the netlib set [9] of linear programming problems. The true solution vector x is taken to be a vector of all ones, and the right hand side is chosen to be y = Ax oeN(0; 1) except the outliers are obtained by adding 100oeN(0; 1) to m 1 (m 1 is number of outliers) randomly chosen elements of y. We set m 1 = 10 in ....

D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13(1985), pp.10-12.

....with own (hybrid) algorithms assembled from the pieces available in the package. A matter of dispute in making experimental computational comparisons is the choice of data sets. The operations research community is well off having public libraries of instances for, e.g. linear programming [Gay85], mixed) integer programming [BBI92] traveling salesman [Rei91] or quadratic assignment [BKR94] Unfortunately, there is not yet such a test set for the minimum capacity cut problem. Moreover, a potential user of a minimum capacity cut algorithm might be interested in problem instances which ....

D.M. Gay (1985), "Electronic mail distribution of linear programming test problems", COAL Newsletter 13, 10--12.

....implementation is a rich source of new algorithmic ideas. Evaluation of optimization software is an important issue for both developers and users. Over the years, libraries of standard test problems have been established that serve this purpose. These libraries are as follows: linear programming [28], quadratic programming (QP) 57] mixed integer programming (MIP) 10] and general nonlinear programming (NLP) 12] These sets are freely available, therefore they are widely used in reporting achievements in algorithmic development. The rationale is one of the basic requirements of scienti c ....

D.M. Gay. Electronic mail distribution of linear programming test problems. COAL Newsletter, 13:10-12, 1985. 30 ###### ###### Optimization Software

....new problems are likely to be even more user oriented than the present ones. Furthermore, because the SIF format is an extension of the MPS linear programming format (see International Business Machines Corporation (1978) access to suites of linear programming test problems (see, for example, Gay (1985)) is possible. Tables 1 and 2 are included to indicate the scope of the applications that are currently represented in the database. Also included are some other test problems of interest to optimization algorithm designers. As can be seen from these tables, many application areas are represented ....

D. M. Gay. Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter, December 1985.

....mapping) KL based mapping heuristics for the graph and hypergraph models. The proposed KL based mapping heuristics are used for the experimental evaluation of the validity of proposed hypergraph model on symmetric sparse matrices selected from HarwellBoeing collection [4] and NETLIB suite [6]. 2 Graph Model of Computation A symmetric sparse matrix A can be represented as an undirected graph GA (V; E) The vertices in the vertex set V correspond to the rows columns of the A matrix. In the edge set E, v i ; v j ) 2E if and only if a ij and a ji of the A matrix are nonzeros. Hence, ....

....algorithms. 5 Experimental Results The proposed one phase KL based mapping heuristics are used for the experimental evaluation of the validity of the proposed hypergraph model on symmetric sparse matrices selected from Harwell Boeing collection [4] and linear programming problems in NETLIB suite [6]. Table 1 illustrates the performance results for the mapping of the selected sparse matrices. BCSPWR06 10 matrices come from the sparse matrix representation of various power networks. JAGMESH9 and LSHP2614 matrices come from the finite element discretizations of pinched hole and L shaped ....

Gay, D. M., "Electronic mail distribution of linear programming test problems" Mathematical Programming Society COAL Newsletter, 1985.

....tree were perfectly balanced, or if only two processors were used for the factorization. local improvements do not result in improving the overall load imbalance. For example, for a wide variety of problems from the Boeing Harwell matrix set and linear programming (LP) matrices from NETLIB [5], even after applying the tree balancing heuristics, the efficiency bound due to load imbalance is still around 80 to 60 [13, 20, 19] If the increased fill in is taken into account, then the maximum achievable efficiency is even lower than that. In the rest of this section we present a ....

D. M. Gay. Electronic Mail Distribution of Linear Programming Test Problems. !mathematical Programming Society COAL Newsletter, December 1985.

....point methods like the predictor corrector method, the normal equation linear system can be written in the form (5) The idea of using low rank modifications (updates or downdates) is not new. In his seminal paper on the first polynomial time interior point method for linear programming, Karmarkar [6] proposed to use low rank modifications to decrease the theoretical complexity bounds. His idea has been pursued by many later papers for the similar reason. On the other hand, a combination of a direct method and an iterative method was reported by Karmarkar and Ramakrishnan [8] Wang and O Leary ....

....and T. Steihaug, Application of a new class of preconditioners to large scale linear programming problems, Presented at The 1999 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications , Minneapolis, Minnesota, USA, June 10 12, 1999. [6] N. Karmarkar, A new polynomial time algorithm for linear programming. Combinatorica, Vol. 4, pp. 373395, 1984. Properties and Computational Issues of a Preconditioner for Interior Point Methods 4 [7] N.K. Karmarkar and K.G. Ramakrishnan, Computational results of an interior point algorithm for ....

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D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, No. 13, pp.10-12, 1985.

....that try to minimize the load imbalance at a given level of the tree. However, very often such local improvements do not result in improving the overall load imbalance. For example, for a wide variety of problems from the Boeing Harwell matrix set and linear programming (LP) matrices from NETLIB [5], even after applying the tree balancing heuristics, the efficiency bound due to load imbalance is still around 80 to 60 [10, 15] If the increased fill in is taken into account, then the maximum achievable efficiency is even lower than that. In the rest of this section we present a ....

D. M. Gay. Electronic Mail Distribution of Linear Programming Test Problems. <mathematical Programming Society COAL Newsletter, December 1985.

.... attempted to cope with rounding errors by introducing a tolerance t (option constraint drop tol, which is 0 by default) and requiring b i b i t or d i d i t before discarding the lower or upper inequality in (5) For example, on the maros test problem of netlib s lp data collection of Gay (1985), under binary IEEE arithmetic, t = 10 13 suffices, whereas the default t = 0 leads to incorrect deductions. Problems in netlib s lp data collection can be fed to AMPL with the help of a model, mps.mod, and awk script, m2a, that are available from netlib. Rather than requiring users to ....

Gay, D. M. (1985), "Electronic Mail Distribution of Linear Programming Test Problems, " COAL Newsletter #13: 10--12.

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Gay, D.M., "Electronic mail distribution of linear programming test problems", COAL Newsletter, Mathematical Programming Society, 13, 1985, p. 10--12.

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D. M. Gay. Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter, 1985.

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D.M. Gay, "Electronic mail distribution of linear programming test problems," Mathematical Programming Society COAL Newsletter, 1985.

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