A line search filter secant method for nonlinear equality constrained optimization |
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Authors: | Zhujun Wang Detong Zhu |
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Institution: | 1.Department of Mathematics,Shanghai Normal University,Shanghai,China;2.Business College,Shanghai Normal University,Shanghai,China |
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Abstract: | This paper formulates and analyzes a line search method for general nonlinear equality constrained optimization based on filter
methods for step acceptance and secant methods for search direction. The feature of the new algorithm is that the secant algorithm
is used to produce a search direction, a backtracking line search procedure is used to generate step size, some filtered rules
are used to determine step acceptance, second order correction technique is used to reduce infeasibility and overcome the
Maratos effect. Global convergence properties of this method are analyzed: under mild assumptions it is showed that every
limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point
that is a stationary point for the problem. Moreover, it is also established that the Maratos effect can be overcome in our
new approach by adding second order correction steps so that fast local superlinear convergence to a second order sufficient
local solution is achieved. Finally, the results of numerical experiments are reported to show the effectiveness of the line
search filter secant method. |
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