Parallelization Strategies of a Row-Action Method for Multicommodity Network Flow Problems

Censor, Yair; Chajakis, Emmanuel D.; Zenios, Stavros A.

doi:10.1080/10637199508915508

Cited by 69 publications

(123 citation statements)

References 24 publications

Supporting

Mentioning

123

Contrasting

Order By: Relevance

“…Algorithms that use regularization based on quadratic or generalized distance functions are called the proximal minimization algorithms; see, e.g., [81, §3.4.3], [72,Ch. 3].…”

Section: Regularized Methodsmentioning

confidence: 99%

“…In the pessimization step, we query oracles for each constraint to determine F i (x), its maximum violation, exactly or approximately. (The oracles for the different constraints can be queried independently and in parallel, allowing a linear speedup of step 2; see, e.g., [72].) Whenever pessimization of a constraint finds a value of u that violates a robust constraint, this value is appended to the list of scenarios for that constraint.…”

Section: Basic Cutting-set Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Cutting-set methods for robust convex optimization with pessimizing oracles

Mutapcic

Boyd

2009

Optimization Methods and Software

132

170

View full text Add to dashboard Cite

We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.

show abstract

“…Algorithms that use regularization based on quadratic or generalized distance functions are called the proximal minimization algorithms; see, e.g., [81, §3.4.3], [72,Ch. 3].…”

Section: Regularized Methodsmentioning

confidence: 99%

Section: Basic Cutting-set Methodsmentioning

confidence: 99%

Cutting-set methods for robust convex optimization with pessimizing oracles

Mutapcic

Boyd

2009

Optimization Methods and Software

132

170

View full text Add to dashboard Cite

show abstract

“…When = 1 the next point is the exact orthogonal projection of the current point. If 0 < < 1, the step taken is shorter (underrelaxation) and if 1 < < 2, then the step taken is longer (overrelaxation) [8].…”

Section: Basic Surrogate Constraint Methods (Bscm)mentioning

confidence: 99%

“…We follow the work [30] and pose the image restoration problem as a linear feasibility problem [8]. The linear feasibility problem asks for a point that satisfies a set of linear inequalities.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parallel image restoration using surrogate constraint methods

Uçar

Aykanat

Pınar

et al. 2007

Journal of Parallel and Distributed Computing

View full text Add to dashboard Cite

When formulated as a system of linear inequalities, the image restoration problem yields huge, unstructured, sparse matrices even for images of small size. To solve the image restoration problem, we use the surrogate constraint methods that can work efficiently for large problems. Among variants of the surrogate constraint method, we consider a basic method performing a single block projection in each step and a coarse-grain parallel version making simultaneous block projections. Using several state-of-the-art partitioning strategies and adopting different communication models, we develop competing parallel implementations of the two methods. The implementations are evaluated based on the per iteration performance and on the overall performance. The experimental results on a PC cluster reveal that the proposed parallelization schemes are quite beneficial.

show abstract

High‐performance numerical pricing methods

Moritsch

Benkner

2002

Concurrency and Computation

View full text Add to dashboard Cite

SUMMARYThe pricing of financial derivatives is an important field in finance and constitutes a major component of financial management applications. The uncertainty of future events often makes analytic approaches infeasible and, hence, time-consuming numerical simulations are required. In the Aurora Financial Management System, pricing is performed on the basis of lattice representations of stochastic multidimensional scenario processes using the Monte Carlo simulation and Backward Induction methods, the latter allowing for the exploitation of shared-memory parallelism. We present the parallelization of a Backward Induction numerical pricing kernel on a cluster of SMPs using HPF+, an extended version of High-Performance Fortran. Based on language extensions for specifying a hierarchical mapping of data onto an SMP cluster, the compiler generates a hybrid-parallel program combining distributed-memory and shared-memory parallelism. We outline the parallelization strategy adopted by the VFC compiler and present an experimental evaluation of the pricing kernel on an NEC SX-5 vector supercomputer and a Linux SMP cluster, comparing a pure MPI version to a hybrid-parallel MPI/OpenMP version.

show abstract

Parallelization Strategies of a Row-Action Method for Multicommodity Network Flow Problems

Cited by 69 publications

References 24 publications

Cutting-set methods for robust convex optimization with pessimizing oracles

Cutting-set methods for robust convex optimization with pessimizing oracles

Parallel image restoration using surrogate constraint methods

High‐performance numerical pricing methods

Contact Info

Product

Resources

About