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A Hybrid Proximal Point Algorithm and a Hundle Method for Solving Nonlinear Variational Inclusions

Author: TangMeng
Tutor: ShenJie
School: Liaoning Normal University
Course: Operational Research and Cybernetics
Keywords: Nonlinear variational inclusion problems Mixed approaching point algorithm (A, η) - Maximal Monotone A - Maximal Monotone Beam method
CLC: O177.1
Type: Master's thesis
Year: 2011
Downloads: 3
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Abstract


Paper is divided into two major discussion variational problem of the existence of the solution containing the problem and how to solve the problem in the first part of generalized resolvent operator theory gives a mixed approaching point algorithm , and using this algorithm studied for a class of nonlinear variational contains the solution of the problem of the existence and solving problems . concrete contains the solution of the problem solving variational process , applied to the concept of generalized resolvent operator specifically with a ? Maximal Monotone related resolvent operator technique , extended to the Hilbert space with ( A , η) ? a maximal monotone related generalized resolvent operator concept . of the mixed impending point algorithm can be gradually approaching the study variables Inclusions solution , after the convergence of the algorithm . similar approach in this part of the final , to solve the problems of a class of generalized nonlinear implicit quasi variational inclusions in the second part , we give for solving generalized variational contains non - smooth beam method , the issues discussed are looking for the real Hilbert space on two the extremal operator and zero . specific method is non - smooth optimization method of beam -beam the method is one of the most effective and the most promising method for solving non - smooth optimization problems , using a series of convex linear function to approximate the sub- problem of non - smooth convex function , the handling of the problem becomes simple and easy to perform . theory stepwise analysis to select the appropriate linear function the θ ~~ i ≤ φ become effective approximation of non- smooth functions . finally stop the use of the guidelines , as well as from the step size tends to zero and away from zero in both cases were discussed convergence of the algorithm in the first case , we require operator is pseudomonotone and multi-valued , the second case , we will have a stronger assumption , that operator requirements is a single value , and to meet a Dunn .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
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