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Projection of a Point onto a Convex Set via Charged Balls Method

In: High-Dimensional Optimization and Probability

Author

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  • Majid E. Abbasov

    (St. Petersburg State University
    Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences)

Abstract

Finding the projection of a point onto a convex set is a problem of computational geometry that plays an essential role in mathematical programming and nondifferentiable optimization. Recently proposed Charged Balls Method allows one to solve this problem for the case when the boundary of the set is given by smooth function. In this chapter, we give an overview of Charged Balls Method and show that the method is applicable also for nonsmooth case. More specifically, we consider the set that is defined by a maximum of a finite number of smooth functions. Obtained results show that even in case of the set with nonsmooth boundary, Charged Balls Method still solves the problem quite competitive effectively in comparison with other algorithms. This is confirmed by the results of numerical experiments.

Suggested Citation

  • Majid E. Abbasov, 2022. "Projection of a Point onto a Convex Set via Charged Balls Method," Springer Optimization and Its Applications, in: Ashkan Nikeghbali & Panos M. Pardalos & Andrei M. Raigorodskii & Michael Th. Rassias (ed.), High-Dimensional Optimization and Probability, pages 1-8, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-00832-0_1
    DOI: 10.1007/978-3-031-00832-0_1
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