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BFGS Method for Nonlinear Monotone Equations with Convex Constraints

Author: ZuoHuaLi
Tutor: WangZhiGuo；XiaoYunHai
School: Henan University
Course: Applied Mathematics
Keywords: Nonlinear equations Quasi-Newton method BFGS method Limited memory BFGS method Global Convergence
CLC: O224
Type: Master's thesis
Year: 2010
Downloads: 52
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Abstract


This thesis solving nonlinear monotone equations BFGS algorithm convex constraints and limited memory BFGS algorithm , to establish the convergence of the algorithm , and solving unconstrained optimization problems , and non-linear numerical experiments verify the effectiveness of the algorithm . equations , quasi-Newton algorithm on the research and development status of the BFGS and limited memory BFGS method ; brief theoretical foundation convex function convex set . proposed solving convex constrained nonlinear monotone equations BFGS method the important feature of this algorithm is no need to calculate the the equations Jocobian matrix ; no need to solve a linear system sub - questions to determine the search direction , and thus can be used to solve the non-smooth equations under appropriate conditions , we demonstrate that the algorithm global convergence through numerical experiments verify the effectiveness of the algorithm . proposed solving convex constrained nonlinear monotone equations limited memory BFGS method , compared to the algorithm in the second chapter , the chapter mentioned algorithm does not require storage matrix , save storage space , speed up the algorithm runs , to improve the numerical efficiency , and thus more likely to be applied to solve large-scale problems . Finally, to prove the global convergence of the algorithm , and large-scale problem of algorithm testing , validation the effectiveness of the algorithm . fourth chapter gives the summary of the thesis , and some continue to explore the direction .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory
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