Approximations for Pareto and Proper Pareto solutions and their KKT conditions
Poonam Kesarwani, Pradyuman K. Shukla, Joydeep Dutta, Kalyanmoy Deb
TL;DR
This paper explores approximate Pareto and proper Pareto solutions in multiobjective optimization, characterizing them via KKT conditions and saddle point concepts, and introduces improved solution concepts with generalized results.
Contribution
It introduces an approximate framework for Pareto and proper Pareto solutions, extending KKT and saddle point characterizations to these approximate solutions in general settings.
Findings
Characterization of approximate Pareto solutions via KKT conditions
Extension of Geoffrion proper solutions to an approximate setting
Generalized results applicable to broader classes of problems
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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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Control Systems Optimization · Advanced Multi-Objective Optimization Algorithms