Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Synthesis of Pareto Optimal Four-Bar Function Generators With Optimum Structural Error and Optimum Transmission Angles

The four-bar function generator solution domain is systematically searched-for mechanisms which exhibit at the same time minimum structural error and the best transmission angles. First, synthesis equations are developed. Then the boundary of the solution domain is defined in terms of the permissible angular changes of the coupler link. The concept of Pareto minima is used to identify potential optimal solutions from a representative sample generated over the solution domain. The procedure is illustrated with an example.