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Modified Bfgs Formula In The Sqp Algorithm

Posted on:2004-11-20Degree:MasterType:Thesis
Country:ChinaCandidate:L JiangFull Text:PDF
GTID:2190360092990488Subject:Computational Mathematics
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In this paper, we are concerned with the sequence quadratic programming (SQP) methods for solving constrained optimization problems. The basic idea of an SQP method is to approximate the constrained problem by a sequence of quadratic programming (QP) problems. The objective function of the QP problem is a quadratic function which is an approximation of the Lagrangian function of the constrained problem and the constraints of the QP problem are linear approximation of the constraints of the constrained problem.In an SQP method, it is important to keep the Hessian of the objective function in QP problem to be positive definite. When the Hessian is positive definite, the QP subproblem is a strict convex quadratic programming. It has a unique solution and can be easily solved by existing algorithms. Moreover, the solution of the QP problem provides a descent direction for most merit functions. Therefore, it is desirable to globalize the method.There have developed some technique to ensure the positive definiteness of the Hessian of the quadratic objective function. However, some of them are restrictive. For some of these methods, the convergence is not knownIn this paper, based on a modified BFGS update formula proposed by Li and Fukushima, we propose a modified BFGS method for solving equality constrained optimization. An attractive property of this method is that the Hessian of the quadratic objective function is always positive definite. Moreover, we show that if the second order sufficient conditions holds at a solution of the problem, then the method is 2-step superlinearly convergent. By using an exact penalty function, we globalize the proposed method. Under appropriate conditions, we obtain the global convergence of the globalized method.
Keywords/Search Tags:equality constrained problem, reduced Hessian method, MBFGS update, 2-step superlinear convergence, superlinear convergence
PDF Full Text Request
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