Weak sharp minima in multiobjective optimization
Weighted means and weighting functions
We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.
Weighted scalarization related to -metric and pareto optimality
Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with -norm related functions (depending on the criteria, goals, and scaling factors) are investigated.