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Constraint qualification in a general class of Lipschitzian mathematical programming problems

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Abstract

The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing the sum of a differentiable function and a locally Lipschitzian function subject to a set of differentiable nonlinear inequalities on a convex subset C of \(\mathbb{R}^{n}\), under the condition of a generalized Kuhn–Tucker constraint qualification or a generalized Arrow–Hurwicz–Uzawa constraint qualification. The case when the set C is open is shown to be a special one of our results, which helps us to improve some of the existing results in the literature. To finish we consider several test problems.

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Authors and Affiliations

  1. Normal School of Jinhua College of Profession and Technology, Jinhua Zhejiang, 321017, People’s Republic of China

    Tong Zishuang

  2. Department of Mathematics, Shanghai University, Baoshan Shanghai, 200444, People’s Republic of China

    X. J. Zheng

Authors
  1. Tong Zishuang
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  2. X. J. Zheng
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Correspondence to Tong Zishuang.

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Zishuang, T., Zheng, X.J. Constraint qualification in a general class of Lipschitzian mathematical programming problems. J Glob Optim 38, 625–635 (2007). https://doi.org/10.1007/s10898-006-9101-5

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  • DOI: https://doi.org/10.1007/s10898-006-9101-5

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