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Structure in Optimization: Factorable Programming and Functions

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Computer and Information Sciences III

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Abstract

It is frequently observed that effective exploitation of problem structure plays a significant role in computational procedures for solving large-scale nonlinear optimization problems. A necessary step in this regard is to express the computation in a manner that exposes the exploitable structure. The formulation of large-scale problems in many scientific applications naturally give rise to “structured” representation. Examples of computationally useful structures arising in large-scale optimization problems include unary functions, partially separable functions, and factorable functions. These structures were developed from 1967 through 1990. In this paper we closely examine commonly occurring structures in optimization with regard to efficient and automatic calculation of first- and higher-order derivatives. Further, we explore the relationship between source code transformation as in algorithmic differentiation (AD) and factorable programming. As an illustration, we consider some classical examples.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Box 7803, 5020 , Bergen, Norway

    Trond Steihaug

  2. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada

    Shahadat Hossain

  3. INRIA, Sophia-Antipolis, France

    Laurent Hascoët

Authors
  1. Trond Steihaug
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  2. Shahadat Hossain
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  3. Laurent Hascoët
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Corresponding author

Correspondence to Trond Steihaug .

Editor information

Editors and Affiliations

  1. , Dept of Electrical and Electronics Eng'g, Imperial College, London, SW7 2BT, United Kingdom

    Erol Gelenbe

  2. , EEE Dept., Imperial College, Exhibition Rd., London, SW72AZ, United Kingdom

    Ricardo Lent

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Steihaug, T., Hossain, S., Hascoët, L. (2013). Structure in Optimization: Factorable Programming and Functions. In: Gelenbe, E., Lent, R. (eds) Computer and Information Sciences III. Springer, London. https://doi.org/10.1007/978-1-4471-4594-3_46

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  • DOI: https://doi.org/10.1007/978-1-4471-4594-3_46

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  • Print ISBN: 978-1-4471-4593-6

  • Online ISBN: 978-1-4471-4594-3

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