LFS functions in multi-objective programming

Luka Neralić; Sanjo Zlobec

Applications of Mathematics (1996)

  • Volume: 41, Issue: 5, page 347-366
  • ISSN: 0862-7940

Abstract

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We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.

How to cite

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Neralić, Luka, and Zlobec, Sanjo. "LFS functions in multi-objective programming." Applications of Mathematics 41.5 (1996): 347-366. <http://eudml.org/doc/32955>.

@article{Neralić1996,
abstract = {We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.},
author = {Neralić, Luka, Zlobec, Sanjo},
journal = {Applications of Mathematics},
keywords = {multi-objective program; efficient (Pareto) solution; properly efficient solution; LFS function; convex program; $l_\{1\}$ norm; $l_\{\infty \}$ norm; simultaneous optimization; Pareto optimality; properly efficient solutions; locally-flat-surface functions},
language = {eng},
number = {5},
pages = {347-366},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {LFS functions in multi-objective programming},
url = {http://eudml.org/doc/32955},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Neralić, Luka
AU - Zlobec, Sanjo
TI - LFS functions in multi-objective programming
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 5
SP - 347
EP - 366
AB - We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.
LA - eng
KW - multi-objective program; efficient (Pareto) solution; properly efficient solution; LFS function; convex program; $l_{1}$ norm; $l_{\infty }$ norm; simultaneous optimization; Pareto optimality; properly efficient solutions; locally-flat-surface functions
UR - http://eudml.org/doc/32955
ER -

References

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