Steepest ascent algorithms for nonconical multiple objective programming

Gordon B. Hazen; Thomas L. Morin

doi:10.1016/0022-247X(84)90075-1

Steepest ascent algorithms for nonconical multiple objective programming

Gordon B. Hazen^*, Thomas L. Morin

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A steepest ascent family of algorithms suitable for the direct solution of continuous variable unconstrained nonconical multiple objective programming problems is introduced. Nonconical multiple objective problems, unlike standard (conical) vector optimization problems, cannot be easily solved by examining related single objective problems. The concept of a direction of steepest ascent is generalized to the multiple objective context and the question of algorithmic convergence is treated. A computational example involving a nonconical unanimity order is given.

Original language	English (US)
Pages (from-to)	188-221
Number of pages	34
Journal	Journal of Mathematical Analysis and Applications
Volume	100
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(84)90075-1
State	Published - Apr 30 1984

Funding

This research was partially supported by National Science Foundation Grant ECS-8105965 to Northwestern University. I wish to thank Martin Czigler, who performed some of the computational work of Section 6.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-247X(84)90075-1

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abstract = "A steepest ascent family of algorithms suitable for the direct solution of continuous variable unconstrained nonconical multiple objective programming problems is introduced. Nonconical multiple objective problems, unlike standard (conical) vector optimization problems, cannot be easily solved by examining related single objective problems. The concept of a direction of steepest ascent is generalized to the multiple objective context and the question of algorithmic convergence is treated. A computational example involving a nonconical unanimity order is given.",

author = "Hazen, {Gordon B.} and Morin, {Thomas L.}",

note = "Funding Information: This research was partially supported by National Science Foundation Grant ECS-8105965 to Northwestern University. I wish to thank Martin Czigler, who performed some of the computational work of Section 6.",

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AU - Morin, Thomas L.

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PY - 1984/4/30

Y1 - 1984/4/30

N2 - A steepest ascent family of algorithms suitable for the direct solution of continuous variable unconstrained nonconical multiple objective programming problems is introduced. Nonconical multiple objective problems, unlike standard (conical) vector optimization problems, cannot be easily solved by examining related single objective problems. The concept of a direction of steepest ascent is generalized to the multiple objective context and the question of algorithmic convergence is treated. A computational example involving a nonconical unanimity order is given.

AB - A steepest ascent family of algorithms suitable for the direct solution of continuous variable unconstrained nonconical multiple objective programming problems is introduced. Nonconical multiple objective problems, unlike standard (conical) vector optimization problems, cannot be easily solved by examining related single objective problems. The concept of a direction of steepest ascent is generalized to the multiple objective context and the question of algorithmic convergence is treated. A computational example involving a nonconical unanimity order is given.

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Steepest ascent algorithms for nonconical multiple objective programming

Abstract

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ASJC Scopus subject areas

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