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A New Fast Convergent SSLE Algorithm For Inequality Constrained Optimization Without Strict Complementarity

Posted on:2007-11-14Degree:MasterType:Thesis
Country:ChinaCandidate:D L HanFull Text:PDF
GTID:2120360185487475Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Sequential Systems of Linear Equations (SSLE) algorithms are widely acknowledged to be among the most successful algorithms for solving nonlinear optimization problems, which are proposed mainly to overcome the defaults of the classical SQP method, such as the consistency problem and large amount of computation effect for solving a QP subproblem. In recent decades, feasible SSLE algorithms have been studied widely, since they have fast rate of convergence, generate feasible iterates, and do not require any quadratic subprogram. However, feasible SSLE algorithms usually require to solve four or five Systems of Linear Equations (SLE) at each iteration, so the computational cost is relatively high. And the strict complementarity condition is necessary, which is strong and difficult for testing.In this paper, a kind of smooth nonlinear optimization problems with inequality constraints is considered, and a new algorithm of SSLE for the problems is proposed by introducing a new constructing technique of the SLE, which recurred to the perturbation of constraints' gradient. Our algorithm includes two cycles of Cycle I and Cycle II. At each iteration of Cycle I, the iterates are all feasible, and at least two reduced SLEs, other than the quadratic programming, need to be solved, while only one SLE is required to be solved in Cycle II. Moreover, we show that the iterative process will enter into Cycle II and never come out this cycle for k large enough, that is, only one SLE needs to be computed after a finite number of iterations. Under mild assumptions without the strict complementarity, it is shown that the proposed algorithm enjoys the properties of global and superlinear convergence. Finally, some preliminary numerical tests are reported, and the numerical results show that only two reduced SLEs with the same coefficient matrix are required to be solved at each iteration of Cycle I for all tested problems, and the amount of computation is much less than other SSLE algorithms.
Keywords/Search Tags:inequality constraints, nonlinear optimization, sequential systems of linear equations, algorithm, convergence
PDF Full Text Request
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