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Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

    X.Q. Yang

  2. Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China

    X.X. Huang

Authors
  1. X.Q. Yang
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  2. X.X. Huang
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Yang, X., Huang, X. Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs. Computational Optimization and Applications 25, 293–311 (2003). https://doi.org/10.1023/A:1022929826650

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