Nonscalarized multiobjective global optimization
Journal of Optimization Theory and Applications
A saddle-point characterization of Pareto optima
Mathematical Programming: Series A and B
A characterization of weakly efficient points
Mathematical Programming: Series A and B
Pareto analysis vis-à-vis balance space approach in multiobjective global optimization
Journal of Optimization Theory and Applications
Equivalence of balance points and Pareto solutions in multiple-objective programming
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Set contraction algorithm for computingpareto set in nonconvex nonsmooth multiobjective optimization
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
Information transmittal, time uncertainty and special relativity
Computers & Mathematics with Applications
Non-causal models in long term planning via set contractive optimal control methods
Mathematical and Computer Modelling: An International Journal
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The notion of balance set is extended onto infinite-dimensional linear spaces. For multiobjective problems of ongoing optima, resource allocation, continuing investment planning with risk forecasting, optimal production models with time-varying objectives, the notion of finite causality is introduced leading to separable programs and sequential (not necessarily convergent) balance and Pareto sets. Selector sequences (or functions for continuous models) are proposed to determine particular Pareto solutions obtained from infinite sequences of the balance set equations. The method is extended onto multicriteria, global optimal control problems, and the use of Schauder bases is made for obtaining monotonic approximations to the sets of balance points and Pareto solutions. An algorithm is tien proposed for computing those approximations and illustrated by a practical example of the bicriteria min-time, min-fuel vertical soft landing problem to facilitate software design.