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<p>We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.</p>

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Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Felipe Lara,
  • Nguyen Van Tuyen,
  • Tran Van Nghi

摘要

We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.