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Study Of Several Algorithms For Solving Nonlinear Optimization Problems

Posted on:2009-10-06Degree:MasterType:Thesis
Country:ChinaCandidate:X R ZhuFull Text:PDF
GTID:2190360272960939Subject:Operational Research and Cybernetics
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The paper is organized as follows: In the first chapter, we briefly review the developing history of SQP method and SSLE method, and introduce some new achievements in this field in recent years. Then the global and locally superlinear convergent conditions are considered and the problems existed in these types of algorithms are presented. At the same time, we also discuss some solutions of these problems. Moreover, we mainly introduce a filter method, which is most widely used in SQP-type method and give some results and new achievements in recent years.In the second chapter, based on a non-smooth equation of KKT optimality condition, this paper presents a new QP-free method for inequality constrained optimization by using the Fischer-Burmeister NCP function. At each iteration, the most three linear equations with the same efficient matrix need to be solved to get the iteration direction. Moreover, the equations involve only constrains in the working set and those not in the working set are totally neglected, which reduces the problem size greatly. Without assuming isolatedness of the accumulation point or boundedness of the Lagrange multiplier approximation sequence, every accumulation point of the iterative sequence generated by this method is a KKT point.In the third chapter, concerning all the problems above mentioned in the existing SSLE algorithms, we propose a new infeasible Filter-SSLE algorithm for NLP. In the new algorithm, the most three linear equations with the same efficient matrix need to be solved to get the iteration direction and it has good global convergence with less computation and weaker assumptions.In the forth chapter, according to a remarkable shortcoming of commonly used exact penalty function in the nonlinear programming problem solution. This chapter considers onemethod of smoothly approaching exact penalty function F1(x,ρ), and gives the errorestimation of smoothing penalty question, non-smooth penalty question as well as the result of objective function in the original question. Basing on the smoothing function, we presents the algorithm of the approximate optimal solution which calculates the problem and the convergences of the algorithm.
Keywords/Search Tags:nonlinear programming, consistence, strict complementarity, SQP, SSLE, second-order sufficient conditions, global convergence, superlinear convergence, Filter, exact penalty function
PDF Full Text Request
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