A Method for Transforming Non-Convex Optimization Problem to Distributed Form

Oleg O. Khamisov, Oleg V. Khamisov (), Todor D. Ganchev () and Eugene S. Semenkin ()
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Oleg O. Khamisov: Depertment of Applied Mathematics, Melentiev Energy Systems Institute, 664033 Irkutsk, Russia
Oleg V. Khamisov: Depertment of Applied Mathematics, Melentiev Energy Systems Institute, 664033 Irkutsk, Russia
Todor D. Ganchev: Department of Computer Science and Engineering, Technical University of Varna, 9010 Varna, Bulgaria
Eugene S. Semenkin: Scientific and Educational Center “Artificial Intelligence Technologies”, Baumann Moscow State Technical University, 105005 Moscow, Russia

Mathematics, 2024, vol. 12, issue 17, 1-16

Abstract: We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups.

Keywords: distributed optimization; non-convex optimization; gradient descent; Newton’s method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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