Nonmonotonic Reduced Projected Hessian Method Via an Affine Scaling Interior Modified Gradient Path for Bounded-Constrained Optimization |
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Authors: | Peihua Guo Detong Zhu |
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Institution: | (1) Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China;(2) Business College, Shanghai Normal University, Shanghai, 200234, China |
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Abstract: | The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic
interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on
variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective
Hessian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using
interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global
convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some
reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned
cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
The research is partially supported by the National Natural Science Foundation of China under Grant No. 10471094, the Ph.D.
Foundation under Grant No. 0527003, the Shanghai Leading Academic Discipline Project (T0401), and the Science Foundation of
Shanghai Education Committee under Grant No. 05DZ11. |
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Keywords: | Affine scaling convergence interior point modified gradient path nonmonotonic technique QR decomposition |
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