C. Choi and Y. Ye, "Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver," Working Paper, Dept. of Management Sciences, The University of Iowa, Iowa IO, USA, March 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....method such as the preconditioned conjugate gradient (PCG) or preconditioned conjugate residual (PCR) method becomes necessary as these methods do not require M to be stored explicitly. Earlier research works on using the PCG or PCR method to solve the SCE arising from large scale SDPs include [6, 18, 20, 21, 31]. As the coe#cient matrix M is dense, traditional preconditioning techniques that are designed for sparse matrices, such as incomplete Cholesky factorizations, cannot be readily applied to M without incurring a significant computational cost and memory usage. Thus in all the above mentioned ....

C. Choi, and Y. Ye, Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver, working paper, Computational Optimization Laboratory, University of Iowa, March, 2000.

....direction without storing the Schur complement matrix in memory. The examples used to test their implementation will also be used in this work to demonstrate the success of the dual scaling method in parallel. Others who have used iterative solvers and preconditioners for SDP include Choi and Ye [12] and Lin and Saigal [20] None of the methods mentioned above have considered the use of parallel processors when implementing methods to solve semidefinite programs. After the initial submission of this paper, Yamashita, Fujisawa, and Kojima[28] presented a parallel implementation of a ....

....PDSPD with the iterative solver needed 4, 944 seconds on one processor and 303 seconds on 32 processors. Using a direct solver, PDSDP needed only 455 and 51 seconds to find a solution. The e#ciency of iterative solvers often depends on good conditioning in the matrix. As noted by many others [12, 22, 25], the matrices are not well conditioned in later iterations and require better preconditioners. Nonetheless, the performance of PDSDP with the iterative solver was competitive on the maximum cut problems. In fact, when more than one processor was used, the iterative solver was faster than the ....

[Article contains additional citation context not shown here]

C. Choi and Y. Ye. Solving sparse semidefinite programs using the dual-scaling algorithm with an iterative solver. Working Paper, Department of Management Science, The University of Iowa, Iowa City, IA, 2000.

....In other words, a key issue here is the scalability of the SDP relaxation approach with respect to the problem size. There have been a great deal of research efforts towards improving the efficiency of SDP solvers, including works on exploiting sparsity in more traditional interior point methods [1, 9, 16, 17, 29] and works on alternative methods [5, 6, 7, 20, 21, 30, 31] Indeed, the efficiency of SDP solvers has been improved significantly in the last few years. Nevertheless, the scalability problem still remains. On the other hand, computational studies have continued to affirm that the quality of ....

....and in Section 6. 5.2. Comparison with DSDP. The second set of test problems are from the so called G set graphs which are randomly generated. Recently, Choi and Ye reported computational results on a subset of G set graphs that were solved as Max Cut problems using their SDP code COPL DSDP [9], or simply DSDP. The code DSDP uses a dual scaling interior point algorithm and an iterative linear RANK 2 RELAXATION FOR BINARY QUADRATIC PROGRAMS 11 Table 5.3 More CirCut Results on Max Cut problems from the Torus Set Graph CirCut (N = 0; M = 100) CirCut (N = 8; M = 100) Name Avg. Val Avg. ....

[Article contains additional citation context not shown here]

C. Choi and Y. Ye. Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver. Working paper, Department of Management Science, University of Iowa, Iowa, 2000.

.... series of papers, we have proposed methods to efficiently solve SDPs for large n (matrix size) On the other hand, the conjugate gradient (CG) method or the conjugate residual (CR) method can be used to solve the system of linear equations (8) when m (number of linear constraints) becomes large [4, 15, 17, 22]. In the CG and CR methods, we need to multiply the coefficient matrix B by a vector several times, instead of computing each element of B and storing them as we did here. Then, we can employ similar algorithms to the ones in subsection 5.2 which explore the sparse factorizations and the sparsity ....

C. Choi and Y. Ye, Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver, Department of Management Sciences, The University of Iowa, Iowa City, IO 52242 March 2000.

.... two series of papers, we have proposed methods to e#ciently solve SDPs for large n (matrix size) On the other hand, the conjugate gradient (CG) method or the conjugate residual (CR) method can be used to solve the system of linear equations (8) when m (number of linear constraints) becomes large [4, 15, 17, 22]. In the CG and CR methods, we need to multiply the coe#cient matrix B by a vector several times, instead of computing each element of B and storing them as we did here. Then, we can employ similar algorithms to the ones in subsection 5.2 which explore the sparse factorizations and the sparsity of ....

C. Choi and Y. Ye, Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver, Department of Management Sciences, The University of Iowa, Iowa City, IO 52242 March 2000.

....number by performing an appropriate preconditioning to M because otherwise even a lower accuracy solution of Mdy = r would require more and more CG or CR iterations. It is a current important issue how we choose an e#ective preconditioning without storing the entire coe#cient matrix M . See [6, 18, 22, 29] for more details on applications of iterative methods, preconditioning and numerical experiments on some large scale SDPs. Another ine#ciency of using primal dual interior point methods is that the nn primal matrix variable X is fully dense in general even when all the data matrices C,A p # S ....

C. Choi and Y. Ye, "Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver," Working Paper, Dept. of Management Sciences, The University of Iowa, Iowa IO, USA, March 2000.

....In a nutshell, the central issue is the scalability of the SDP relaxation approach with respect to the problem size. There have been a great deal of research e#orts towards improving the e#ciency of SDP solvers, including works on exploiting sparsity in more traditional interior point methods [1, 8, 12, 13, 22] and works on alternative methods [3, 4, 5, 6, 15, 16, 23, 24] Indeed, the e#ciency of SDP solvers has been improved significantly in the last few years. Nevertheless, the scalability problem still remains. Can the scalability problem of the SDP relaxation be overcome Can the SDP relaxation ....

....0.538 41684852 g3 15 253522848 0.154 264732800 277864512 7.880 281029888 The second set of test problems are from the so called G set graphs. Recently, Choi and Ye reported computational results on a subset of G set graphs that were solved as Max Cut problems using their SDP code COPL DSDP [8], or simply DSDP. The code DSDP uses a dual scaling interior point algorithm and an iterative linear equation solver. It is currently one of the fastest interior point codes for solving SDP problems. We feel that it is appropriate for us to compare with DSDP, not as a competing code, but rather as ....

[Article contains additional citation context not shown here]

C. Choi and Y. Ye. Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver. Working paper, Department of Management Science, University of Iowa, Iowa, 2000.

....In a nutshell, the central issue is the scalability of the SDP relaxation approach with respect to the problem size. There have been a great deal of research efforts towards improving the efficiency of SDP solvers, including works on exploiting sparsity in more traditional interior point methods [1, 8, 12, 13, 23] and works on alternative methods [3, 4, 5, 6, 15, 16, 24, 25] Indeed, the efficiency of SDP solvers has been improved significantly in the last few years. Nevertheless, the scalability problem still remains. Can the scalability problem of the SDP relaxation be overcome Can the SDP relaxation ....

....0.538 41684814 g3 15 253522848 0.154 264732800 277864512 7.880 281029888 The second set of test problems are from the so called G set graphs. Recently, Choi and Ye reported computational results on a subset of G set graphs that were solved as Max Cut problems using their SDP code COPL DSDP [8], or simply DSDP. The code DSDP uses a dual scaling interior point algorithm and an iterative linear equation solver. It is currently one of the fastest interior point codes for solving SDP problems. We feel that it is appropriate for us to compare with DSDP, not as a competing code, but rather as ....

[Article contains additional citation context not shown here]

C. Choi and Y. Ye. Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver. Working paper, Department of Management Science, University of Iowa, Iowa, 2000.

....matrix M by performing an appropriate preconditioning to M because otherwise even a lower accuracy solution of Mdy = r would require more and more CG or CR iterations. It is a current important issue how we choose an effective preconditioning without storing the entire coefficient matrix M . See [6, 19, 22, 28] for more details on applications of iterative methods, preconditioning and numerical experiments on some large scale SDPs. Another inefficiency of using primal dual interior point methods is that the n Theta n primal matrix variable X is fully dense in general even when all the data matrices A p ....

C. Choi and Y. Ye, "Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver," Comb. Optim. Lab., Univ. of Iowa, 2000.

....the dual scaling method of Benson et al. 2] does not give superior performance on our feasibility problems at this time. However, at the time of writing significant progress has been made with these methods by using a conjugate gradient method to solve the Newton system at each iteration [4]. Dual scaling methods therefore remain a promising alternative. 4 Computational results: detecting unsatisfiability for (2 p) SAT This section contains a selection of computational results we have obtained for random (2 p) SAT formulae. In particular, the following figures indicate the ....

C. Choi and Y. Ye. Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver Working paper, Computational Optimization LAb, Dept. of Management Science, University of Iowa, Iowa City, USA, 2000. 17

No context found.

C. Choi and Y. Ye, "Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver," Working Paper, Dept. of Management Sciences, The University of Iowa, Iowa IO, USA, March 2000.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC