GAMS/LGO Nonlinear Solver Suite: Key Features, Usage, and Numerical Performance
CitationResearch report, PCS Inc., Halifax, NS, Canada; November 2003. Submitted for publication.ArticleDownload View PDF
Optimization Software and Modeling Systems
A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix Completion
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 … Read more
Parallel Strategies for GRASP with path-relinking
A Greedy Randomized Adaptive Search Procedure (GRASP) is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. We analyze two parallel strategies for GRASP with path-relinking and propose a criterion … Read more
A Grid-Enabled Distributed Branch-and-Bound Algorithm with
This work introduces a distributed branch-and-bound algorithm to be run on computational Grids. Grids are often organized in a hierarchical fashion: clusters of processors connected via high-speed links, while the clusters themselves are geographically distant and connected through slower links. Our algorithm does not employ the usual master-worker paradigm and it considers the hierarchical structure … Read more
A Semidefinite Programming Approach for the Nearest Correlation Matrix Problem
The nearest \cm\ problem is to find a positive semidefinite matrix with unit diagonal that is nearest in the Frobenius norm to a given symmetric matrix $A$. This problem can be formulated as an optimization problem with a quadratic objective function and semidefinite programming constraints. Using such a formulation, we derive and test a primal-dual … Read more
Parallel Interior Point Solver for Structured Quadratic Programs: Application to Financial Planning Problems
Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is … Read more
A methodology for the analysis of parallel GRASP strategies
In this paper, we describe a methodology for the analysis of greedy randomized adaptive search procedures (GRASP). GRASP is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and a local search. Hybrid approaches of GRASP with path-relinking developed for the 3-index assignment problem (AP3) and … Read more
A Server for Automated Performance Analysis of Benchmarking Data
As part of Performance World, we describe an automation server (PAVER: http://www.gamsworld.org/performance/paver) to help facilitate reproducible performance analysis of benchmarking data for optimization software. Although PAVER does not solve optimization problems, it automates the task of performance data analysis and visualization, taking into account various performance metrics. These include not only robustness and efficiency, but … Read more
The Use of Java Arrays for Matrix Computations
In the paper it is shown how to utilize the flexibility in native Java arrays for matrix computations. Suitable datastructures for symmetric and sparse matrices are introduced. A disadvantage of the native Java arrays is shown when used as two-dimensional array for dense matrix computation. Numerical results show that the efficiency is not lost using … Read more
Linear Programming support in WSMP
The Watson Sparse Matrix Package (WSMP) is a high-performance robust direct solver for both symmetric and unsymmetric large sparse systems of linear equations. Currently, it works in serial, multi-threaded parallel, message-passing parallel, and a combination of message-passing and multi-threaded modes on IBM RS6000 with AIX and IA32 with Linux. The symmetric solver has features to … Read more