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LFS functions in multi-objective programming. (English) Zbl 0870.90090

The authors investigate a convex multi-criteria constrained mathematical program: Minimize \(\Phi ^k(x)\) subject to \(f^i(x)\leq 0\) and \(x\to \mathbb R^n,\) where \(k\) and \(i\) range finite index sets. Sufficient conditions guaranteeing the coincidence of the set of Pareto optimal solutions with the set of properly efficient solutions are isolated; such a coincidence means that each Pareto solution enjoys additional uniform stability properties. These conditions are based on a notion of (nonsmooth) functions with ”locally flat surfaces” (abbreviated as LFS functions). The results are illustrated on an example from a shape of a road design where a (discrete version) of \(L^\infty \)- and \(L^1\)-norms are to be optimized simultaneously, which leads naturally to a two-criteria program.

MSC:

90C29 Multi-objective and goal programming
49N60 Regularity of solutions in optimal control
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References:

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