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<p>M-stationarity, which involves the limiting (Mordukhovich or basic) normal cone has proved having various advantages, for instance in comparison with KKT optimality conditions; even if Fritz John optimality condition is considered. We actually show an example of an optimization problem where solutions are localized exclusively via M-stationarity. This paper deals with geometric constraint sets (named quadric surfaces or simply quadric) that are determined by a quadratic function, and presents a formula for the limiting normal cone, which is not necessarily the union of polyhedra, to the union of two quadric surfaces. Afterwards, we establish local uniqueness and sensitivity results in nonconvex quadratic programming in the context of M-stationarity.</p>

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Limiting Normal Cone to Quadric Surfaces, Local Uniqueness and Error Bound in M-stationarity

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Fabián Flores-Bazán,
  • Filip Thiele,
  • Dinh Hoang Nguyen

摘要

M-stationarity, which involves the limiting (Mordukhovich or basic) normal cone has proved having various advantages, for instance in comparison with KKT optimality conditions; even if Fritz John optimality condition is considered. We actually show an example of an optimization problem where solutions are localized exclusively via M-stationarity. This paper deals with geometric constraint sets (named quadric surfaces or simply quadric) that are determined by a quadratic function, and presents a formula for the limiting normal cone, which is not necessarily the union of polyhedra, to the union of two quadric surfaces. Afterwards, we establish local uniqueness and sensitivity results in nonconvex quadratic programming in the context of M-stationarity.