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Harnessing Trend Theory to Enhance Distributed proximal point algorithm Approaches for Multi-Area Economic Dispatch Optimization

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Computers, Materials & Continua 2025年第3期82卷 4503-4533页

作者： Yaming Ren Xing Deng College of Mechanical and Control Engineering Guilin University of TechnologyGuilin541006China School of Computer Jiangsu University of Science and TechnologyZhenjiang212003China

The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power *** complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly *** the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization *** proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs *** study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the *** PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence ***,the convergence efficiency of the PPA is significantly influenced by the parameter *** address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational *** computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch *** simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.

关键词： Multi-area economic dispatch problem proximal point algorithm trend theory

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proximal point algorithm FOR MINIMIZATION OF DC FUNCTION

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Journal of Computational Mathematics 2003年第4期21卷 451-462页

作者： Wen-yuSun Raimundo.J.B.Sampaio M.A.B.Candido SchoolofMathematicsandComputerScience NanjingNormalUniversityNanjing2100g7China ProgramadePos-GraduacaoemInformaticaAplicada PontificiaUniversidadeCatolicadoParana(PUCPR)CEP:80215-g01CuritibaPRBrazil ProgramadePos-GraduacaoemInformaticaAplicada PontificiaUniversidadeCatolicadoParana(PUCPR)CEP:80215-g01CuritibaPRBrazil

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferential and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.

关键词： Nonconvex optimization Nonsmooth optimization DC function proximal point algorithm ε-subgradient.

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proximal point algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis

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MATHEMATICAL MODELLING AND ANALYSIS 2016年第1期21卷 95-118页

作者： Promluang, Khanittha Sitthithakerngkiet, Kanokwan Kumam, Poom KMUTT Dept Math Fac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ North Bangkok KMUTNB Fac Sci Appl Dept Math Nonlinear Dynam Anal Res Ctr 1518 Pracharat 1 Rd Bangkok 10800 Thailand KMUTT Theoret & Computat Sci TaCS Ctr Fac Sci Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand China Med Univ 91 Hsueh Shih Rd Taichung 40402 Taiwan

In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2 uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.

关键词： proximal point algorithm Zero point inverse strongly accretive operator nonexpansive mapping

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proximal point algorithm for inclusion problems in Hadamard manifolds with applications

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OPTIMIZATION LETTERS 2021年第3期15卷 901-921页

作者： Ansari, Qamrul Hasan Babu, Feeroz Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran Saudi Arabia

This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed. Applications to composite minimization problems and variational inequality problems are also presented.

关键词： Inclusion problems proximal point algorithm Composite minimization problems Variational inequality problems Maximal monotone vector fields Hadamard manifolds

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proximal point algorithm for Quasi-Convex Minimization Problems in Metric Spaces

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2018年第4期39卷 438-448页

作者： Khatibzadeh, Hadi Mohebbi, Vahid Univ Zanjan Dept Math POB 45195-313 Zanjan Iran

In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove -convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.

关键词： -convergence Hadamard space metric convergence minimization proximal point algorithm quasi-convex

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proximal point algorithm for infinite pseudo-monotone bifunctions

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OPTIMIZATION 2016年第8期65卷 1629-1639页

作者： Khatibzadeh, Hadi Mohebbi, Vahid Univ Zanjan Dept Math Zanjan Iran

In this paper, first we study the weak convergence of the proximal point algorithm for an infinite family of equilibrium problems of pseudo-monotone type in Hilbert spaces. Then with additional conditions on the bifunctions, we prove the strong convergence for the family to a common equilibrium point. We also study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point of the family of infinite pseudo-monotone bifunctions without any additional assumptions on the bifunctions. A concrete example of a family of pseudo-monotone bifunctions is also presented.

关键词： Equilibrium problem pseudo-monotone bifunction proximal point algorithm weak convergence strong convergence Halpern's method

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proximal point algorithm with Schur decomposition on the cone of symmetric semidefinite positive matrices

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2009年第2期355卷 469-478页

作者： Gregorio, Ronaldo Oliveira, Paulo Roberto Univ Fed Rio de Janeiro Comp & Syst Engn Dept BR-21945970 Rio De Janeiro Brazil

In this work, we propose a proximal algorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programming problems on the cone of diagonal definite positive matrices that has the structure of the positive orthant of the Euclidian vector space. We are motivated by results of the classical proximal algorithm extended to Riemannian manifolds with nonpositive sectional curvature. An important example of such a manifold is the space of symmetric definite positive matrices, where the metrics is given by the Hessian of the standard barrier function -In det(X). Observing the obvious fact that proximal algorithms do not depend on the geodesics, we apply those ideas to develop a proximal point algorithm for convex functions in this Riemannian metric. (c) 2009 Elsevier Inc. All rights reserved.

关键词： proximal point algorithm Hadamard manifold Schur decomposition Complete metric space Riemannian mean

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proximal point algorithm for nonlinear multivalued type mappings in Hadamard spaces

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2019年第17期42卷 5758-5768页

作者： Kumam, Wiyada Kitkuan, Duangkamon Padcharoen, Anantachai Kumam, Poom Rajamangala Univ Technol Thanyaburi RMUTT Fac Sci & Technol Dept Math & Comp Sci Program Appl Stat Thanyaburi Thailand KMUTT KMUTT Fixed Point Res Lab KMUTT Fixed Point Theory & Applicat Res Grp Theoret & Computat Sci Ctr TaCS 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT Dept Math Fac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan

In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Delta-convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.

关键词： CAT(0) spaces common fixed points convex minimization problems nonlinear multivalued mappings proximal point algorithm

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Entropy-Like Minimization Methods Based On Modified proximal point algorithm

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INFOR 2014年第3期52卷 147-156页

作者： Hamdi, Abdelouahed Bnouhachem, Abdellah Qatar Univ Dept Math Stat & Phys Doha Qatar Nanjing Univ Sch Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Ibn Zohr Univ ENSA Agadir Morocco

In this paper we introduce an extension of the proximal point algorithm proposed by Guler for solving convex minimization problems. This extension is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic entropy-like distances, called phi-divergences. A study of the convergence rate of this new proximal point method under mild assumptions is given, and further it is shown that this estimate rate is better than the available one of proximal-like methods. Some applications are given concerning general convex minimizations, linearly constrained convex programs and variationnal inequalities.

关键词： proximal point algorithm interior proximal methods nonquadratic regularizations variationnal inequalities

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A customized proximal point algorithm for convex minimization with linear constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第3期56卷 559-572页

作者： He, Bingsheng Yuan, Xiaoming Zhang, Wenxing Nanjing Univ Int Ctr Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Hong Kong Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.

关键词： Convex minimization proximal point algorithm Resolvent operator Augmented Lagrangian method

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