Geodesic
LFS functions in multi-objective programming
Applications of Mathematics, Tome 41 (1996) no. 5, pp. 347-366
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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.
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.
DOI : 10.21136/AM.1996.134331
Classification : 41A28, 49N60, 90C29
Keywords: multi-objective program; efficient (Pareto) solution; properly efficient solution; LFS function; convex program; $l_{1}$ norm; $l_{\infty }$ norm; simultaneous optimization 
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Neralić, Luka; Zlobec, Sanjo. LFS functions in multi-objective programming. Applications of Mathematics, Tome 41 (1996) no. 5, pp. 347-366. doi: 10.21136/AM.1996.134331

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