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  • 1
    Electronic Resource
    Electronic Resource
    Vectorization and multitasking of nonlinear network programming algorithms (1988)
    Springer
    Mathematical programming 42 (1988), S. 449-470 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Vector supercomputers are designed with two levels of parallelism in order to achieved computational efficiency: low level parallelism through vector operations and high level parallelism with multiple independent processors. These innovations have a significant impact on the development of algorithms for network optimization. In this paper a framework for the vectorization and multitasking of optimization software is developed. It is then applied on the primal truncated Newton algorithm for nonlinear generalized network problems. The vectorization and multitasking of the algorithm is discussed and illustrated with computational experiments with the software system NLPNETG on the CRAY series of vector multiprocessors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589416
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  • 2
    Electronic Resource
    Electronic Resource
    An interior point method with Bregman functions for the variational inequality problem with paramonotone operators (1998)
    Springer
    Mathematical programming 81 (1998), S. 373-400 
    Details
    ISSN: 1436-4646
    Keywords: Variational inequalities ; Monotone operators ; Paramonotone operators ; Convex programming ; Generalized distances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an algorithm for the variational inequality problem on convex sets with nonempty interior. The use of Bregman functions whose zone is the convex set allows for the generation of a sequence contained in the interior, without taking explicitly into account the constraints which define the convex set. We establish full convergence to a solution with minimal conditions upon the monotone operatorF, weaker than strong monotonicity or Lipschitz continuity, for instance, and including cases where the solution needs not be unique. We apply our algorithm to several relevant classes of convex sets, including orthants, boxes, polyhedra and balls, for which Bregman functions are presented which give rise to explicit iteration formulae, up to the determination of two scalar stepsizes, which can be found through finite search procedures. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580089
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  • 3
    Electronic Resource
    Electronic Resource
    Proximal minimizations with D-functions and the massively parallel solution of linear network programs (1993)
    Springer
    Computational optimization and applications 1 (1993), S. 375-398 
    Details
    ISSN: 1573-2894
    Keywords: network programs ; parallel computing ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper discusses the massively parallel solution of linear network programs. It integrates the general algorithmic framework of proximal minimization with D-functions (PMD) with primal-dual row-action algorithms. Three alternative algorithmic schemes are studied: quadratic proximal point, entropic proximal point, and least 2-norm perturbations. Each is solving a linear network problem by solving a sequence of nonlinear approximations. The nonlinear subproblems decompose for massively parallel computing. The three algorithms are implemented on a Connection Machine CM-2 with up to 32K processing elements, and problems with up to 16 million variables are solved. A comparison of the three algorithms establishes their relative efficiency. Numerical experiments also establish the best internal tactics which can be used when implementing proximal minimization algorithms. Finally, the new algorithms are compared with an implementation of the network simplex algorithm executing on a CRAY Y-MP vector supercomputer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00248763
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  • 4
    Electronic Resource
    Electronic Resource
    Data parallel computing for network-structured optimization problems (1994)
    Springer
    Computational optimization and applications 3 (1994), S. 199-242 
    Details
    ISSN: 1573-2894
    Keywords: Parallel optimization ; networks ; data structures ; large-scale computations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Data level parallelism is a type of parallelism whereby operations are performed on many data elements concurrently, by many processors. These operations are (more or less) identical, and are executed in a synchronous, orderly fashion. This type of parallelism is used by massively parallel SIMD (i.e., Single Instruction, Multiple Data) architectures, like the Connection Machine CM-2, the AMT DAP and Masspar, and MIMD (i.e., Multiple Instruction, Multiple Data) architectures, like the Connection Machine CM-5. Data parallelism can also be described by a theoretical model of computation: the Vector-Random Access Machine (V-RAM). In this paper we discuss practical approaches to the data-parallel solution of large scale optimization problems with network—or embedded-network—structures. The following issues are addressed: (1) The concept of dataparallelism, (2) algorithmic principles that lead to data-parallel decomposition of optimization problems with network—or embedded-network—structures, (3) specific algorithms for several network problems, (4) data-structures needed for efficient implementations of the algorithms, and (5) empirical results that highlight the performance of the algorithms on a data-parallel computer, the Connection Machine CM-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299446
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  • 5
    Electronic Resource
    Electronic Resource
    A Scalable Parallel Interior Point Algorithm for Stochastic Linear Programming and Robust Optimization (1997)
    Springer
    Computational optimization and applications 7 (1997), S. 143-158 
    Details
    ISSN: 1573-2894
    Keywords: planning under uncertainty ; parallel computing ; optimization ; software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure is employed that exploits the structure of the constraint matrix, and it is implemented on parallel computers. The implementation is perfectly scalable. Extensive computational results are reported for a library of standard test problems from stochastic linear programming, and also for robust optimization formulations.The results show that the codes are efficient and stable for problems with thousands of scenarios. Test problems with 130 thousand scenarios, and a deterministic equivalent linear programming formulation with 2.6 million constraints and 18.2 million variables, are solved successfully.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008675930362
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  • 6
    Electronic Resource
    Electronic Resource
    Mean-absolute deviation portfolio optimization for mortgage-backed securities (1993)
    Springer
    Annals of operations research 45 (1993), S. 433-450 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We develop an integrated simulation/optimization model for managing portfolios of mortgage-backed securities. The mortgage portfolio problem is viewed in the same spirit of models used for the management of portfolios of equities. That is, it trades off rates of return with a suitable measure of risk. In this respect we employ amean-absolute deviation model which is consistent with the asymmetric distribution of returns of mortgage securities and derivative products. We develop a simulation procedure to compute holding period returns of the mortgage securities under a range of interest rate scenarios. The simulation explicitly takes into account the stylized facts of mortgage securities: the propensity of homeowners to prepay their mortgages, and theoption adjusted premia associated with these securities. Details of both the simulation and optimization models are presented. The model is then applied to the funding of a typical insurance liability stream, and it is shown to generate superior results than the standardportfolio immunization approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02282062
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  • 7
    Electronic Resource
    Electronic Resource
    Preface (1988)
    Springer
    Annals of operations research 14 (1988), S. IX 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186470
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  • 8
    Electronic Resource
    Electronic Resource
    Asset/liability management under uncertainty for fixed-income securities (1995)
    Springer
    Annals of operations research 59 (1995), S. 77-97 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Short-sighted asset/liability strategies of the seventies left financial intermediaries — banks, insurance and pension fund companies, and government agencies — facing a severe mismatch between the two sides of their balance sheet. A more holistic view was introduced with a generation ofportfolio immunization techniques. These techniques have served the financial services community well over the last decade. However, increased interest rate volatilities, and the introduction of complex interest rate contingencies and asset-backed securities during the same period, brought to light the shortcomings of the immunization approach. This paper describes a series of (optimization) models that take a global view of the asset/liability management problem using interest rate contingencies. Portfolios containingmortgage-backed securities provide the typical example of the complexities faced by asset/liability managers in a volatile financial world. We use this class of instruments as examples for introducing the models. Empirical results are used to illustrate the effectiveness of the models, which become increasingly more complex but also afford the manager increasing flexibility.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031744
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  • 9
    Electronic Resource
    Electronic Resource
    On the use of expert systems in network optimization: With an application to matrix balancing (1989)
    Springer
    Annals of operations research 20 (1989), S. 111-140 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Network optimization models have a wide variety of applications in operations research, management science, transportation, engineering design and other areas. Much has been done on the design of efficient algorithms for the solutions of very large problems. Difficulties remain, however, in building and implementing such models on the computer for practical use. Notwithstanding, recent developments in modelling languages, building network models remains the privilege of experienced modellers and is in general a time-consuming task. Expert systems and artificial intelligence methodologies could provide the link between practitioners and network optimization techniques. In this paper, we examine the role of expert systems in an operations research environment and identify the issues to be addressed in developing an expert system for network modelling. The discussion is illustrated with the development of a prototype expert system that solves matrix balancing problems using network optimization techniques. The system has the ability to identify the correct (nonlinear) network optimization model for each problem instance. A network problem is automatically set up and solved using a high-level modelling language. The results of the model and sensitivity analysis information are interpreted for the user by the expert system, in the vocabulary of the original description of the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02216925
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Vector and parallel computing for matrix balancing (1990)
    Springer
    Annals of operations research 22 (1990), S. 161-180 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Estimating the entries of a large matrix to satisfy a set of internal consistency relations is a problem with several applications in economics, urban and regional planning, transportation, statistics and other areas. It is known as theMatrix Balancing Problem. Matrix balancing applications arising from the estimation of telecommunication or transportation traffic and from multi-regional trade flows give rise to huge optimization problems. In this report, we show that the RAS algorithm can be specialized for vector and parallel computing and used for the solution of very large problems. The algorithm is specialized for vector computations on a CRAY X-MP and is parallelized on an Alliant FX/8. A variant of the algorithm — developed here for its potential parallelism — turns out to be more efficient than the original algorithm even when implemented serially. We use the algorithms to estimate disaggregated input/output tables and a multi-regional trade flow table of the U.S. The larger problem solved has approximately 12 000 constraints and over 370 000 nonlinear variables. This is the first of two papers that aim at the solution of very large matrix balancing problems. Zenios [20] is using the same algorithm for the same models on a massively parallel Connection Machine CM-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023052
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