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<p>In this work, the notions of <i>normal cones at infinity</i> to unbounded sets and <i>limiting and singular subdifferentials at infinity</i> for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results.</p>

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Subdifferentials at infinity and applications in optimization

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • Do Sang Kim,
  • Minh Tùng Nguyen,
  • Tien-Son Pham

摘要

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results.