Many practical large-scale optimization problems are not only sparse, but also display some form of block-structure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is block-structured itself. Problems with these characteristics appear frequently in stochastic programming but also in other areas such as telecommunication network modelling. We present a linear algebra library tailored for problems with such structure that is used inside an interior point solver for convex quadratic programming problems. Due to its object-oriented design it can be used to exploit virtually any nested block structure arising in practical problems, eliminating the need for highly specialised linear algebra modules needing to be written for every type of problem separately. Through a careful implementation we achieve almost automatic parallelisation of the linear algebra. The efficiency of the approach is illustrated on several problems arising in the financial planning, namely in the asset and liability management. The problems are modelled as

We present an integrated procedure to build and solve big stochastic programming models. The individual components of the system --the modeling language, the solver and the hardware-- are easily accessible, or a least affordable to a large audience. The procedure is applied to a simple financial model, which can be expanded to arbitrarily large sizes by enlarging the number of scenarios. We generated a model with one million scenarios, whose deterministic equivalent linear program has 1,111,112 constraints and 2,555,556 variables. We have been able to solve it on the cluster of ten PCs in less than 3 hours. Key words. Algebraic modeling language, decomposition methods, distributed systems, large-scale optimization, stochastic programming. 1 Introduction Practical implementations of stochastic programming involve two big challenges. First, we have to build the model: its size is almost invariably large, if not huge, and this task is in itself a challenge for This research was suppor...

: Extracting complex block structures from an anonymous mathematical program is a difficult task. It is however a mandatory step to exploit them with adequate algorithmic techniques. Moreover, most economic models are usually built with an Algebraic Modeling Language (AML) which loose any structure. The recently developed concept SET (Structure Exploiting Tool) responds to these needs. This approach relates directly to the "semantic" of the original model that was used to generate the corresponding anonymous mathematical program. Examples from stochastic programming are presented. Copyright c fl1998 IFAC Keywords: Decomposition methods, Modelling, Parallel algorithms, Stochastic programming, Structured programming. 1. INTRODUCTION Many economic models based on mathematical programming may display complex nested block structures. Unfortunately, it remains difficult to exploit these structures within algebraic modeling languages. Thanks to the concept SET (Structure Exploiting Tool) (Fra...

We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct models from sub-models, and is implemented as a combination of preand post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decomposition-based solvers can therefore directly take advantage of the problem’s structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum. 1

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report here on a deterministic equivalent linear programming model of 1,111,112 constraints and 2,555,556 variables generated by GAMS. It is solved by an interior point based decomposition method in less than 3 hours on a cluster of 10 Linux PC's. Key words. Algebraic modeling language, distributed systems, financial planning, large scale optimization, structure exploiting solver. 1 Introduction The curse of dimensionality is a major problem in optimization. To depict real life situations with greater accuracy, optimization models tend to be larger and larger, a trend that is probably encouraged by the rapid development of cheap and powerful computers. Unfortunately, hardware improvements This research was supported by the Fonds National de la Recherche Scientifique Suisse, grants #12-4250...

SETSTOCH is a tool for linking Algebraic Modeling Languages (AMLs) with Specialized Stochastic Programming Solvers (SSPSs). Its main role is to retrieve from the AML a dynamically ordered core model (baseline scenario) that is then sent automatically to the SSPS. The user is then able to take full advantage of speciøc SSPS features. The current implementation of SETSTOCH enables to access the SP/OSL subroutines via the GAMS modeling language. An example of energy planning is presented. Key words: algebraic modeling language, decomposition algorithm, energy modeling, stochastic programming, structure exploiting solver. 1 Introduction Nowadays, the modeler has powerful tools to build eoeective mathematical programming problems: Algebraic Modeling Languages (AMLs). However, when future events are to be considered, it may be pertinent to specify uncertain parameters directly in the model. The corresponding branch of mathematical programming is also known as stochastic programming (see [3...

this paper that by an efficient management of multiple indexed sets, within an algebraic modeling language, it is possible to extract easily customized block structures. Extracting complex block structures from an unstructured mathematical program is a difficult task. It is however a mandatory step to exploit them with adequate algorithmic techniques. Several heuristics exist that can detect automatically certain special forms. Although interesting work has been undertaken (see for instance [13]), detecting a block structure from an unstructured MP remains an NP complete problem. Moreover, in case of very complex forms such as nested block structures, some doubt can be raised about their potential efficiency. If the cost incurred by the extraction of special forms exceeds the gains obtained to exploit them, then this approach is not attractive anymore. An alternative is to refer directly to the "semantic" of the original model. We focus here on multistage stochastic programming problems with recourse since they combine two main dimensions: time and randomness. We should insist that we could have chosen other problems as an illustration. The work on both dimensions allows us to customize precisely the shape of the desired structure (e.g., staircase structure, simple or nested dual block-angular structures) and the sizes of blocks involved). It is indeed difficult to determine in advance which shape benefits at best from a given structure exploiting solver. In order to extract and exploit different block structures within the algebraic modeling language, we employ the concept SET [16] that stands for Structure Exploiting Tool. SET is made up of two distinctive parts. SPI (Structure Passing Interface) extracts the 3 structure desired by the modeler. Then SES (Structure E...

This paper presents a new tool to include uncertainty management in energy and environmental

this paper, we describe a new collection of MINLP test models that is available through a new web site called "MINLP World" (http://www.gamsworld.org/minlp). We have attacked problems both of format and of confidentiality by using a new model translator built into the GAMS system. This translator and its output are described in Section 2. Information about the MINLP library ("MINLPLib") is provided in Section 3, and Section 4 contains additional information about the MINLP initiative, and presents our conclusions

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