A method for minimization of piecewise quadratic functions with lower and upper bounds

One of the main problems in development the decision support software is the availability of efficient optimization algorithms. These algorithms, when applied in decision support systems should possess several features -- like robustness, efficiency and high speed. All these facts motivated the System and Decision Sciences Program to investigate all these topics. The paper presents the result of a collaborative research made at the Systems Research Institute of the Polish Academy of Sciences. This research is being performed upon a contracted study agreement between the IIASA and the Polish Academy of Sciences. The presented algorithm will be included as an option in the HYBRID package implemented on IIASA computers: running UNIX (on Sun Sparc and on VAX 6210) and on PC IBM AT compatible

User Guide to a Mathematical Programming Package for Multicriteria Dynamic Linear Problems Hybrid Version 3.1

This paper is one of the series of 11 Working Papers presenting the software for interactive decision support and software tools for developing decision support systems. These products constitute the outcome of the contracted study agreement between the System and Decision Sciences Program at IIASA and several Polish scientific institutions. The theoretical part of these results is presented in the IIASA Working Paper WP-88-071 entitled "Theory, Software and Testing Examples in Decision Support Systems", which contains the theoretical and methodological backgrounds of the software system developed within the project. This paper presents the HYBRID system for solving linear multiple criteria optimization problems, utilizing the reference point technique. This method, originally developed by the authors, is the non-simplex one and is based on the augmented Lagrangian technique with conjugate gradient optimization. Due to special properties of the method it was possible to make the implementation especially efficient for solving dynamic problems. In such cases the HYBRID outperforms such known packages, like MINOS. Since the method does not require to store large amount of information (like basis matrix in standard Simplex formulation) it is especially valuable for microcomputer applications, allowing to solve problems a magnitude bigger dimensionality than with standard methods

Implementation of an Algorithm for Scaling Matrices and Other Programs Useful in Linear Programming

Matrix scaling is an operation in which the rows and columns of a matrix are multiplied by positive scalars such that the elements of the scaled matrix are similar in absolute magnitude. This can be very important when dealing with models in which matrix elements can take a wide range of values, especially since certain mathematical codes, such as MINOS, require that the absolute values of all non-zero elements should be "reasonably" close to one. This paper describes the implementation of an optimal scaling method proposed by Curtis and Reid. The algorithm is outlined and a users' guide to the program implemented on the VAX at IIASA is given. (The scaling algorithm has been linked to the MINOS package at IIASA by Zenon Fortuna, who has also developed a rescaling routine linked to this package.) Two other programs useful in linear programming are also described: the first is designed to print out a matrix by rows, and also gives diagnostic aid; the second makes it possible to merge up to five LP models into one, generating a resultant MPSX file that may be used to solve multicriteria problems

A Mathematical Programming Package for Multicriteria Dynamic Linear Problems HYBRID. Methodological and User Guide to Version 3.03

One of the main problems in development the decision support software is the availability of efficient optimization algorithms. These algorithms, when applied in decision support systems should possess several criteria -- like robustness, efficiency, high speed and low memory requirements. Moreover, the special structure of the optimization problem arising in such applications should be taken into account. All these facts motivated the System and Decision Sciences Program to investigate all these topics. This paper presents the result of such collaborative effort. The HYBRID system, developed in the Institute of System Research of the Polish Academy of Sciences is the implementation of original, non simplex algorithm especially suited for solving dynamic multiple criteria problem. Except of high efficiency, this algorithm is especially interesting for microcomputers with small available memory. This research is being performed upon a contracted study agreement between the International Institute for Applied Systems Analysis and the Polish Academy of Sciences

HYBRID - A Mathematical Programming Package

This paper describes a new mathematical programming package developed by the authors and implemented both on the VAX at IIASA and at the Computing Center of the State Planning Commission in Warsaw. The new package, called HYBRID, is designed for the solution of linear programming problems, making use of a particular implementation of the Lagrange multiplier method. The version described here is limited to static LP problems (including multiobjective problems that may be reformulated as LP problems), but it will eventually be extended to deal with dynamic problems. HYBRID is intended for use with real-world problems that require scenario analysis. and is therefore oriented towards an interactive mode of operation in which a sequence of problems is to be solved under different conditions (e.g., with different objective functions, reference points, constraints or bounds). This report provides all the information necessary to use the HYBRID package at IIASA and also discusses the methodological issues associated with the chosen solution technique

Coordination of Sectoral Production Planning Using Prices and Quotas (A Case Study for the Polish Agricultural Model)

Understanding the nature and dimensions of the world food problem and the policies available to alleviate it has been the focal point of the IIASA Food and Agriculture Program since it began in 1977. National food systems are highly interdependent, and yet the major policy options exist at the national level. Therefore, to explore these options, it is necessary both to develop policy models for national economies and to link them together by trade and capital transfers. For greater realism the models in this scheme are being kept descriptive, rather than normative. In the end it is proposed to link models to twenty countries, which together account for nearly 80 per cent of important agricultural attributes such as area, production, population, exports, imports and so on. As part of the development of the Polish Agricultural Model, Marek Makowski and Janusz Sosnowski have investigated the coordination of sectoral production planning in Poland. Since this work involved methodological innovations, it was carried out in joint collaboration with the Food and Agriculture Program (FAP) and the Systems and Decision Sciences Area of IIASA. This paper presents intermediate results of research done within the framework of the elaboration of the Polish Agricultural model, which will not only be included in the system of models of the FAP, but will also be used for decision-making processes in Poland