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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 standard multiple criteria optimization starts with an
assumption that the criteria are incomparable. However, there are many
applications in which the criteria express ideas of allocation of
resources meant to achieve some equitable distribution. This paper
focuses on solving linear multiple criteria optimization problems with
uniform criteria treated in an equitable way. An axiomatic definition of
equitable efficiency is introduced as an refinement of
Pareto-optimality. Various generation...
The present paper studies the following constrained vector optimization problem: , , , where , are locally Lipschitz functions, is function, and and are closed convex cones. Two types of solutions are important for the consideration, namely -minimizers (weakly efficient points) and -minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point to be a -minimizer and first-order sufficient conditions for ...
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