# LFS functions in multi-objective programming

Applications of Mathematics (1996)

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

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topNeralić, 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 -

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