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Strongly nonlinear multivalued boundary value problems

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2003年第4期52卷 1219-1238页

作者： Gasinski, L Papageorgiou, NS Jagiellonian Univ Inst Comp Sci PL-30072 Krakow Poland Natl Tech Univ Athens Dept Math Athens 15780 Greece

In this paper we study nonlinear second-order differential inclusions involving the differential operator depending on both: unknown function x and its derivative x', a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and can be applied to the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the "convex" and "nonconvex" problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： maximal monotone operator pseudomonotone operator Hartman condition vector p-Laplacian convex and nonconvex problems periodic problems Neumann problem Dirichlet problem

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Nonlinear second-order multivalued boundary value problems

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PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 2003年第3期113卷 293-319页

作者： Gasinski, L Papageorgiou, NS Natl Tech Univ Athens Dept Math Athens 15780 Greece Jagiellonian Univ Inst Comp Sci PL-30072 Krakow Poland

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the 'convex' and 'nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.

关键词： maximal monotone operator pseudomonotone operator Hartman condition vector p-Laplacian convex and nonconvex problems Leray-Schauder alternative

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A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization problems

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2008年第10期19卷 1665-1677页

作者： Barbarosou, Maria P. Maratos, Nicholas G. Natl Tech Univ Athens Sch Elect & Comp Engn GR-15773 Athens Greece

In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t -> infinity. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate.

关键词： Constrained optimization convergence convex and nonconvex problems recurrent neural networks

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A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION

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Journal of Computational Mathematics 2018年第6期36卷 881-902页

作者： Cheng Chen Zaiwen Wen Yaxiang Yuan University of Chinese Academy of Sciences Beijing 100190 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Beijing International Center for Mathematical Research Peking University Beijing 100871 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.

关键词： Nonlinear optimization convex and nonconvex problems Subspace technique Multigrid/multilevel method Large-scale problems

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An efficient global technique for solving the network constrained static and dynamic economic dispatch problem

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2017年第1期25卷 73-82页

作者： Nawaz, Aamir Saleem, Nasir Mustafa, Ehtasham Khan, Umair Ali Gomal Univ Fac Engn & Technol Dept Elect Engn Dera Ismail Khan Khyber Pakhtunk Pakistan Pakistan Navy Ordnance Training Sch Karachi Pakistan

This paper presents a new approach for solving Economic Load Dispatch (ELD) problem with generator constraints and transmission losses. Constrained Globalized Nelder Mead (CGNM) is a new proposed algorithm for solving economic dispatch problem with and without valve point effects. convex and Non-convex cost functions with equality and inequality constraints are difficult to optimize. To circumvent these problems, a robust global technique is desirable. In this paper, Constrained Globalized Nelder Mead is proposed to optimize Economic Load Dispatch (ELD) problem globally using Variance Variable Probability (VVP). To validate the proficiency of proposed approach, statistical studies have been accomplished for different test systems of Static Economic Dispatch (ED) that is 3-unit convex and non-convex systems without losses 6-unit convex system with losses, 13-unit non-convex systems without losses and 20-unit non-convex system without losses. Also, proposed model proficiency is verified by applying it on Dynamic Economic Dispatch for test systems that is 3-unit convex system with no losses and 5-unit non-convex system with losses. Comparison of proposed algorithm with other optimization algorithms, reported in literature depicts that proposed algorithm is quite robust.

关键词： Globalized Nelder-Mead static and dynamic economic dispatch convex and nonconvex problems valve point effects

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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

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Acta Mathematica Scientia 2024年第4期44卷 1280-1300页

作者： Zhenhai LIU Nikolaos S.PAPAGEORGIOU Center for Applied Mathematics of Guangri Yulin Normal UniversityYulin 537000China Guangri Key Laboratory of Universities Optimization Control and Engineering Calculation College of Mathematics and PhysicsGuangri Minzu UniversityNanning 530006China Department of Mathematics National Technical UniversityZografou Campus15780 AthensGreece

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued *** prove the existence theorems for both the convex and nonconvex *** also show the existence of extremal periodic solutions and provide a strong relaxation ***,we provide an application to nonlinear periodic control systems.

关键词： periodic boundary condition time-dependent maximal monotone operator convex and nonconvex problems extremal solutions strong relaxation

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Extremal solutions and strong relaxation for second order multivalued boundary value problems

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CZECHOSLOVAK MATHEMATICAL JOURNAL 2005年第4期55卷 827-844页

作者： Gasinski, L Papageorgiou, NS Jagiellonian Univ Inst Comp Sci PL-30072 Krakow Poland Natl Tech Univ Athens Dept Math Athens 15780 Greece

In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, ... 详细信息

关键词： maximal monotone operator pseudomonotone operator Hartman condition convex and nonconvex problems extremal solutions strong relaxation

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Nonlinear multivalued Duffing systems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2018年第1期468卷 376-390页

作者： Papageorgiou, Nikolaos S. Vetro, Calogero Vetro, Francesca Natl Tech Univ Athens Dept Math Zografou Campus Athens 15780 Greece Univ Palermo Dept Math & Comp Sci Via Archirafi 34 I-90123 Palermo Italy Ton Due Thang Univ Nonlinear Anal Res Grp Ho Chi Minh City Vietnam Ton Due Thang Univ Fac Math & Stat Ho Chi Minh City Vietnam

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski [7]. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Duffing system Nonlinear differential operator convex and nonconvex problems Relaxation Continuous and measurable selections Fixed point

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Existence and Relaxation Results for Second Order Multivalued Systems

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ACTA APPLICANDAE MATHEMATICAE 2021年第1期173卷 5-5页

作者： Papageorgiou, Nikolaos S. Vetro, Calogero Natl Tech Univ Athens Dept Math Zografou Campus Athens 15780 Greece Univ Palermo Dept Math & Comp Sci Via Archirafi 34 I-90123 Palermo Italy

We consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term A(x) and of a multivalued perturbation F(t, x, y) which can be convex or nonconvex valued. We consider the cases where D(A) not equal R-N and D(A) = R-N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

关键词： Maximal monotone map convex and nonconvex problems Continuous and measurable selections Relaxation Optimal control

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