Radial solutions and orthogonal trajectories in multiobjective global optimization

Radial solutions and orthogonal trajectories in multiobjective global optimization

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Article ID: iaor20031167
Country: Netherlands
Volume: 115
Issue: 2
Start Page Number: 315
End Page Number: 344
Publication Date: Nov 2002
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming: multiple criteria
Abstract:

This paper presents a new, ray-oriented method for the global solution of nonscalarized vector optimization problems and a framework for the application of the Karush–Kuhn–Tucker theorem to such problems. Properties of nonlinear multiobjective problems implied by the Karush–Kuhn–Tucker necessary conditions are investigated. The regular case specific to nonscalarized MOPs is singled out when a nonlinear MOP with nonlinearities only in the constraints reduces to a nondegenerate linear system. It is shown that the trajectories of the Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of the vector deviations in the balance space (to the balance set for Pareto solutions). Illustrative examples are presented.

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