Convergence and Speed of the Inexact Proximal Point Algorithm with Quasi-distance

Huamán Ñaupa J.L.; Papa Quiroz E.A.; Quispe Infantes R.R. · Revista Politecnica (2026) · DOI: 10.33333/rp.vol57n1.06

Resumen

The convergence and speed of the rate of convergence of a sequence generated by an algorithm are relevant in the computational complexity for the solution of optimization problems applied to several areas as economics, engineering and artificial intelligence. In this work, the convergence and rate of convergence of the sequence generated by the inexact proximal point algorithm (IPA) with quasi-distance to a critical point of functions that satisfy the Kurdyka Lojasiewicz (KL) conditions are determined. The used methodology is the analysis of convergence of the generated sequence using elements of topology in the Euclidean space. It is proved that the convergence and several types of speed of convergence for a family of concave functions given in the KL condition. These results may be used in applications where the convexity of the problem is not assured.

Instituciones: Universidad Nacional Mayor de San Marcos; Universidad Nacional de San Cristóbal de Huamanga; Universidad Nacional José María Arguedas