A computational study of transformation methods for optimal design

Ashok D. Belegundu, Jasbir S. Arora

    Research output: Contribution to journalArticle

    31 Citations (Scopus)

    Abstract

    In this paper computational aspects of transformation methods are studied. Transformation methods, which include sequential unconstrained minimization techniques (SUMTs) and multiplier methods, are based on solving a sequence of unconstrained minimization problems. An efficient technique is given to compute gradients of the transformation function. An operations count is given to demonstrate savings of the suggested technique over two other techniques used in the literature. Computer programs implementing the use of this technique in SUMTs and multiplier algorithms are developed. Applications of these programs on a set of structural design problems are given. Multiplier methods are found to be very stable and reliable, even on some relatively difficult problems, and they perform better than SUMTs. Some ways of improving the efficiency of transformation methods are given, together with possible extensions of using the suggested approach to compute gradients of implicit functions.

    Original languageEnglish (US)
    Pages (from-to)535-542
    Number of pages8
    JournalAIAA Journal
    Volume22
    Issue number4
    DOIs
    StatePublished - Jan 1 1984

    Fingerprint

    Structural design
    Computer program listings
    Optimal design

    All Science Journal Classification (ASJC) codes

    • Aerospace Engineering

    Cite this

    Belegundu, Ashok D. ; Arora, Jasbir S. / A computational study of transformation methods for optimal design. In: AIAA Journal. 1984 ; Vol. 22, No. 4. pp. 535-542.
    @article{869458531abb468d8b9599d7186a4055,
    title = "A computational study of transformation methods for optimal design",
    abstract = "In this paper computational aspects of transformation methods are studied. Transformation methods, which include sequential unconstrained minimization techniques (SUMTs) and multiplier methods, are based on solving a sequence of unconstrained minimization problems. An efficient technique is given to compute gradients of the transformation function. An operations count is given to demonstrate savings of the suggested technique over two other techniques used in the literature. Computer programs implementing the use of this technique in SUMTs and multiplier algorithms are developed. Applications of these programs on a set of structural design problems are given. Multiplier methods are found to be very stable and reliable, even on some relatively difficult problems, and they perform better than SUMTs. Some ways of improving the efficiency of transformation methods are given, together with possible extensions of using the suggested approach to compute gradients of implicit functions.",
    author = "Belegundu, {Ashok D.} and Arora, {Jasbir S.}",
    year = "1984",
    month = "1",
    day = "1",
    doi = "10.2514/3.48476",
    language = "English (US)",
    volume = "22",
    pages = "535--542",
    journal = "AIAA Journal",
    issn = "0001-1452",
    publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",
    number = "4",

    }

    A computational study of transformation methods for optimal design. / Belegundu, Ashok D.; Arora, Jasbir S.

    In: AIAA Journal, Vol. 22, No. 4, 01.01.1984, p. 535-542.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A computational study of transformation methods for optimal design

    AU - Belegundu, Ashok D.

    AU - Arora, Jasbir S.

    PY - 1984/1/1

    Y1 - 1984/1/1

    N2 - In this paper computational aspects of transformation methods are studied. Transformation methods, which include sequential unconstrained minimization techniques (SUMTs) and multiplier methods, are based on solving a sequence of unconstrained minimization problems. An efficient technique is given to compute gradients of the transformation function. An operations count is given to demonstrate savings of the suggested technique over two other techniques used in the literature. Computer programs implementing the use of this technique in SUMTs and multiplier algorithms are developed. Applications of these programs on a set of structural design problems are given. Multiplier methods are found to be very stable and reliable, even on some relatively difficult problems, and they perform better than SUMTs. Some ways of improving the efficiency of transformation methods are given, together with possible extensions of using the suggested approach to compute gradients of implicit functions.

    AB - In this paper computational aspects of transformation methods are studied. Transformation methods, which include sequential unconstrained minimization techniques (SUMTs) and multiplier methods, are based on solving a sequence of unconstrained minimization problems. An efficient technique is given to compute gradients of the transformation function. An operations count is given to demonstrate savings of the suggested technique over two other techniques used in the literature. Computer programs implementing the use of this technique in SUMTs and multiplier algorithms are developed. Applications of these programs on a set of structural design problems are given. Multiplier methods are found to be very stable and reliable, even on some relatively difficult problems, and they perform better than SUMTs. Some ways of improving the efficiency of transformation methods are given, together with possible extensions of using the suggested approach to compute gradients of implicit functions.

    UR - http://www.scopus.com/inward/record.url?scp=0021411430&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0021411430&partnerID=8YFLogxK

    U2 - 10.2514/3.48476

    DO - 10.2514/3.48476

    M3 - Article

    VL - 22

    SP - 535

    EP - 542

    JO - AIAA Journal

    JF - AIAA Journal

    SN - 0001-1452

    IS - 4

    ER -