2019•arXiv (Cornell University)Open access

Approximations for Pareto and Proper Pareto solutions and their KKT conditions

Poonam Kesarwani, Pradyuman K. Shukla, Joydeep Dutta, Kalyanmoy Deb

Abstract

In this article, we view the approximate version of Pareto and weak Pareto solutions of the multiobjective optimization problem through the lens of KKT type conditions. We also focus on an improved version of Geoffrion proper Pareto solutions and characterize them through saddle point and KKT type conditions. We present an approximate version of the improved Geoffrion proper solutions and propose our results in general settings.

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Key concepts: Karush–Kuhn–Tucker conditions, Pareto principle, Saddle point, Mathematical optimization, Focus (optics), Type (biology), Point (geometry), Pareto optimal