Two Error Bounds for Constrained Optimization Problems and Their Applications

Journal Article · Sun Jun 15 04:00:00 EDT 2008 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-007-9023-8· OSTI ID:21242048

Jianzhong, Zhang ^[1]; Wenling, Zhao ^[2]

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1. City University of Hong Kong, Department of Mathematics (Hong Kong)
2. Shandong University of Technology, School of Mathematics (China)

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.

• OSTI ID: 21242048
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 57; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
ERRORS
FUNCTIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROGRAMMING
OPTIMIZATION