Optimality Conditions for Pareto-Optimal Solutions

Vladimir Gorbunov; Elena Sinyukova

doi:10.4028/www.scientific.net/KEM.685.142

Paper Titles

Decay of Low-Barrier Metastable State: Middle Friction
p.124

Corrections to Kramers Formula Describing the Decay Rate of a Metastable State
p.128

Bending Process Simulation of a Flat Workpiece with Various Cross-Sectional Mechanical Properties with PAM-STAMP 2G
p.133

Identification Method of Blast-Furnace Process Parameters
p.137

Optimality Conditions for Pareto-Optimal Solutions
p.142

Initial Data Forming for Process Simulation in System “Intruder – Physical Protection System”
p.148

Numerical Modeling of Cyclone Machine for Cleaning Gas Generator Gases
p.153

Simulation of Conditions of Solid Fossil Fuels Formation for Underground Conversion Investigation
p.158

Numerical Study of Grain Evolution and Dislocation Density during Asymmetric Rolling of Aluminum Alloy 7075
p.162

HomeKey Engineering MaterialsKey Engineering Materials Vol. 685Optimality Conditions for Pareto-Optimal Solutions

Optimality Conditions for Pareto-Optimal Solutions

Abstract:

In this paper the authors describe necessary conditions of optimality for continuous multicriteria optimization problems. It is proved that the existence of effective solutions requires that the gradients of individual criteria were linearly dependent. The set of solutions is given by system of equations. It is shown that for finding necessary and sufficient conditions for multicriteria optimization problems, it is necessary to switch to the single-criterion optimization problem with the objective function, which is the convolution of individual criteria. These results are consistent with non-linear optimization problems with equality constraints. An example can be the study of optimal solutions obtained by the method of the main criterion for Pareto optimality.

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High Technology: Research and Applications 2015

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Key Engineering Materials (Volume 685)

Pages:

142-147

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.685.142

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Online since:

February 2016

Authors:

Vladimir Gorbunov, Elena Sinyukova

Keywords:

Effective Solutions, Multicriteria Optimization, Necessary Conditions for Local Optimization, Pareto Optimality, Sufficient Conditions for Local Optimization

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