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Keywords:
multi-objective program; efficient (Pareto) solution; properly efficient solution; LFS function; convex program; $l_{1}$ norm; $l_{\infty }$ norm; simultaneous optimization
multi-objective program; efficient (Pareto) solution; properly efficient solution; LFS function; convex program; $l_{1}$ norm; $l_{\infty }$ norm; simultaneous optimization
Summary:
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.
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