Accelerated convergence for the Powell/Hestenes multiplier method |
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Authors: | Krisorn Jittorntrum |
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Institution: | (1) Asian Institute of Technology, Bangkok, Thailand;(2) Computing Research Group, Australian National University, Canberra, A.C.T., Australia |
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Abstract: | It is known that augmented Lagrangian or multiplier methods for solving constrained optimization problems can be interpreted as techniques for maximizing an augmented dual functionD
c( ). For a constantc sufficiently large, by considering maximizing the augmented dual functionD
c( ) with respect to , it is shown that the Newton iteration for based on maximizingD
c( ) can be decomposed into taking a Powell/Hestenes iteration followed by a Newton-like correction. Superimposed on the original Powell/Hestenes method, a simple acceleration technique is devised to make use of information from the previous iteration. For problems with only one constraint, the acceleration technique is equivalent to replacing the second (Newton-like) part of the decomposition by a finite difference approximation. Numerical results are presented. |
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Keywords: | Nonlinear Programming Constrained Optimization Augmented Lagrangian Methods Multiplier Methods |
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