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ITERATIVE ALGORITHMS FOR SYSTEM OF VARIATIONAL INCLUSIONS IN hadamard manifolds

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Acta Mathematica Scientia 2022年第4期42卷 1333-1356页

作者： Qamrul Hasan ANSARI Feeroz BABU D.R.SAHU Department of Mathematics Aligarh Muslim UniversityAligarh202002India Department of Applied Mathematics Aligarh Muslim UniversityAligarh202002India Department of Mathematics Banaras Hindu UniversityVaranasi 221005India

In this paper,we consider system of variational inclusions and its several spacial cases,namely,alternating point problems,system of variational inequalities,etc.,in the setting of hadamard *** propose an iterative algorithm for solving system of variational inclusions and study its convergence *** special cases of the proposed algorithm and convergence result are also *** present application to constraints minimization problems for bifunctions in the setting of hadamard *** the end,we illustrate proposed algorithms and convergence analysis by a numerical *** algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to hadamard manifolds.

关键词： System of variational inclusions altering point problems monotone vector fields strictly pseudocontractive mappings hadamard manifolds

On the Convergence Rate of a Proximal Point Algorithm for Vector Function on hadamard manifolds

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Journal of the Operations Research Society of China 2017年第3期5卷 405-417页

作者： Feng-Mei Tang Ping-Liang Huang College of Science Shanghai UniversityShanghai 200444China

The proximal point algorithm has many interesting applications,such as signal recovery,signal processing and *** recent years,the proximal point method has been extended to Riemannian *** main advantages of these extensions are that nonconvex problems in classic sense may become geodesic convex by introducing an appropriate Riemannian metric,constrained optimization problems may be seen as unconstrained *** this paper,we propose an inexact proximal point algorithm for geodesic convex vector function on hadamard *** the assumption that the objective function is coercive,the sequence generated by this algorithm converges to a Pareto critical *** the objective function is coercive and strictly geodesic convex,the sequence generated by this algorithm converges to a Pareto optimal ***,under the weaker growth condition,we prove that the inexact proximal point algorithm has linear/superlinear convergence rate.

关键词： Inexact proximal point algorithm hadamard manifolds Convergence rate Pareto critical point Pareto optimal point

On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on hadamard manifolds

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Journal of the Operations Research Society of China 2017年第4期5卷 457-467页

作者： Nancy Baygorrea Erik Alex Papa Quiroz Nelson Maculan Federal University of Rio de Janeiro PESC-COPPE-UFRJPO Box 68511Rio de Janeiro CEP 21941-972Brazil

In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on hadamard *** prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.

关键词： Proximal point method Quasiconvex function hadamard manifolds Nonsmooth optimization Abstract subdifferential Convergence rate

Inexact Proximal Point Methods for Quasiconvex Minimization on hadamard manifolds

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Journal of the Operations Research Society of China 2016年第4期4卷 397-424页

作者： Nancy Baygorrea Erik Alex Papa Quiroz Nelson Maculan Federal University of Rio de Janeiro PESC-COPPE-UFRJPO Box 68511Rio de Janeiro CEP 21941-972Brazil

In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on hadamard *** prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the *** also present an application of the method to demand theory in economy.

关键词： Proximal point method Quasiconvex function hadamard manifolds Nonsmooth optimization Abstract subdifferential