Two Error Bounds for Constrained Optimization Problems and Their Applications |
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Authors: | Chang-Yu Wang Jian-Zhong Zhang Wen-Ling Zhao |
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Institution: | (1) Institute of Operations Research, Qufu Normal University, Qufu, Shandong, China;(2) Department of Mathematics, City University of Hong Kong, Hong Kong, Hong Kong;(3) School of Mathematics, Shandong University of Technology, Zibo, Shandong, China |
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Abstract: | This paper presents a global error bound for the projected gradient and a local error bound for the distance from a feasible
solution to the optimal solution set of a nonlinear programming problem by using some characteristic quantities such as value
function, trust region radius etc., which are appeared in the trust region method. As applications of these error bounds,
we obtain sufficient conditions under which a sequence of feasible solutions converges to a stationary point or to an optimal
solution, respectively, and a necessary and sufficient condition under which a sequence of feasible solutions converges to
a Kuhn–Tucker point. Other applications involve finite termination of a sequence of feasible solutions. For general optimization
problems, when the optimal solution set is generalized non-degenerate or gives generalized weak sharp minima, we give a necessary
and sufficient condition for a sequence of feasible solutions to terminate finitely at a Kuhn–Tucker point, and a sufficient
condition which guarantees that a sequence of feasible solutions terminates finitely at a stationary point.
This research was supported by the National Natural Science Foundation of China (10571106) and CityU Strategic Research Grant. |
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Keywords: | Trust region subproblem Value function Projected gradient Error bound Finite termination |
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