Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/15497
Title: Partially strictly monotone and nonlinear penalty functions for constrained mathematical programs
Authors: Yang, XQ 
Huang, XX
Keywords: Constrained mathematical program
Convergence analysis
Nonlinear penalty function
Optimality condition
Partially strictly monotone function
Issue Date: 2003
Publisher: Springer
Source: Computational optimization and applications, 2003, v. 25, no. 1-3, p. 293-311 How to cite?
Journal: Computational optimization and applications 
Abstract: We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.
URI: http://hdl.handle.net/10397/15497
ISSN: 0926-6003
EISSN: 1573-2894
DOI: 10.1023/A:1022929826650
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