SDPLIB 1.2, a library of semidefinite programming test problems

Borchers, Brian

doi:10.1080/10556789908805769

Cited by 105 publications

(111 citation statements)

References 5 publications

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“…Finally, in column f is the value of the objective function obtained. Looking at table 3, we can see that the numbers of iterations are comparable to the size of of the problem (except for hinf 8, hinf 14 and qap6) and the value of the objective function is similar to the values published in [11].…”

Section: Numerical Examplesmentioning

confidence: 53%

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A feasible direction interior point algorithm for nonlinear semidefinite programming

Aroztegui

Herskovits

Roche

et al. 2014

Struct Multidisc Optim

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We present a new algorithm for nonlinear semidefinite programming. It is based on the iterative solution, in the primal and dual variables, of KarushKuhn-Tucker first order optimality conditions. This method generates a decreasing feasible sequence. At each iteration, two linear systems with the same coefficient matrix are solved and an inexact line search is then performed. A proof of global convergence is given in the convex case. Some numerical tests involving nonlinear programming problems as well linear and nonlinear matrix inequalities are described. We also solve structural topology optimization problems employing a mathematical model based on semidefinite programming. The results suggest efficiency and high robustness of the proposed method.

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Section: Numerical Examplesmentioning

confidence: 53%

“…Test problems from SDP LIB and COM P l e ib Here we present some results with test problems of SDP LIB [11]. SDPLIB is a collection of linear semidefinite programming test problems.…”

Section: Numerical Examplesmentioning

confidence: 99%

A feasible direction interior point algorithm for nonlinear semidefinite programming

Aroztegui

Herskovits

Roche

et al. 2014

Struct Multidisc Optim

View full text Add to dashboard Cite

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“…The experimental setup for performance evaluation is summarized in Table 2 and dense matrices are extracted from SDPLIB [12] benchmarks shown in Table 3. We implement the proposed architecture in VHDL and synthesize the circuit for Xilinx Virtex6-SX475T FPGA, a device with the largest number of DSP48Es and a large on-chip capacity.…”

Section: Methodsmentioning

confidence: 99%

“…1. We pick small to medium size matrices from SDPLIB [12], a collection of benchmarks for solving SDPs, and use Intel MKL library for sequential implementation on an Intel Xeon X5650. We show the runtime distribution in Fig.…”

Section: Sequential Runtime Analysismentioning

confidence: 99%

A High Throughput FPGA-Based Implementation of the Lanczos Method for the Symmetric Extremal Eigenvalue Problem

Rafique

Kapre

Constantinides

2012

Lecture Notes in Computer Science

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Abstract. Iterative numerical algorithms with high memory bandwidth requirements but medium-size data sets (matrix size ∼ a few 100s) are highly appropriate for FPGA acceleration. This paper presents a streaming architecture comprising floating-point operators coupled with highbandwidth on-chip memories for the Lanczos method, an iterative algorithm for symmetric eigenvalues computation. We show the Lanczos method can be specialized only for extremal eigenvalues computation and present an architecture which can achieve a sustained single precision floating-point performance of 175 GFLOPs on Virtex6-SX475T for a dense matrix of size 335×335. We perform a quantitative comparison with the parallel implementations of the Lanczos method using optimized Intel MKL and CUBLAS libraries for multi-core and GPU respectively. We find that for a range of matrices the FPGA implementation outperforms both multi-core and GPU; a speed up of 8.2-27.3× (13.4× geo. mean) over an Intel Xeon X5650 and 26.2-116× (52.8× geo. mean) over an Nvidia C2050 when FPGA is solving a single eigenvalue problem whereas a speed up of 41-520× (103× geo.mean) and 131-2220× (408× geo.mean) respectively when it is solving multiple eigenvalue problems.

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“…In section 4.3 we investigate how the sparsity of the extended sparsity pattern of an SDP affects the efficiency of the three software packages. And finally in sections 4.4 and 4.5 we select a number of SDPs from the SDPLIB [6] problems and DIMACS challenge problems and solve them using SDPARA-C. Table 4. In this table, n and m respectively represent the size of matrix variables X and Y and the number of linear constraints in the primal problem (1).…”

Section: Numerical Experimentsmentioning

confidence: 99%

A parallel primal–dual interior-point method for semidefinite programs using positive definite matrix completion

2006

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Abstract. A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of its coefficient matrix. SDPARA can effectively solve SDPs with a large number of equality constraints, however, it does not solve SDPs with a large scale matrix variable with similar effectiveness. SDPA-C is a primal-dual interior-point method using the positive definite matrix completion technique by Fukuda et al, and it performs effectively with SDPs with a large scale matrix variable, but not with a large number of equality constraints. SDPARA-C benefits from the strong performance of each of the two methods. Furthermore, SDPARA-C is designed to attain a high scalability by considering most of the expensive computations involved in the primal-dual interior-point method. Numerical experiments with the three parallel software packages SDPARA-C, SDPARA and PDSDP by Benson show that SDPARA-C efficiently solve SDPs with a large scale matrix variable as well as a large number of equality constraints with a small amount of memory.

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SDPLIB 1.2, a library of semidefinite programming test problems

Cited by 105 publications

References 5 publications

A feasible direction interior point algorithm for nonlinear semidefinite programming

A feasible direction interior point algorithm for nonlinear semidefinite programming

A High Throughput FPGA-Based Implementation of the Lanczos Method for the Symmetric Extremal Eigenvalue Problem

A parallel primal–dual interior-point method for semidefinite programs using positive definite matrix completion

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