Title :
Quadratic image of a ball: Towards efficient description of the boundary
Author :
Polyak, Boris ; Shcherbakov, Pavel ; Khlebnikov, Mikhail
Author_Institution :
Lab. of Adaptive & Robust Control Syst., Inst. of Control Sci., Moscow, Russia
Abstract :
We propose a simple efficient machinery for computing “nearly exact” boundary of the image of euclidean ball under multidimensional quadratic mapping. It is based on necessary conditions for a point to be mapped to the boundary. Several special cases are considered, the results of numerical simulations are presented, in particular, as applied to multiobjective optimization and Pareto set discovery.
Keywords :
Pareto optimisation; computational geometry; set theory; Euclidean ball image; Pareto set discovery; ball quadratic image; boundary description; multidimensional quadratic mapping; multiobjective optimization; numerical simulation; Approximation methods; Eigenvalues and eigenfunctions; Equations; Generators; Symmetric matrices; Transmission line matrix methods; Vectors; Convexity; Euclidean ball; Necessary conditions; Pareto front; Quadratic mappings;
Conference_Titel :
System Theory, Control and Computing (ICSTCC), 2014 18th International Conference
Conference_Location :
Sinaia
DOI :
10.1109/ICSTCC.2014.6982399
