SIAM Journal on Optimization, Volume 30, Issue 3, Page 2603-2627, January 2020.
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of Demyanov--Rubinov--Polyakova quasidifferentials under the minimal possible assumptions. To this end, we obtain a novel description of convex subcones of the contingent cone to a set defined by quasidifferentiable equality and inequality constraints with the use of a new constraint qualification. We utilize this description and constraint qualification to derive the strongest existing optimality conditions for nonsmooth mathematical programming problems in terms of quasidifferentials under less restrictive assumptions than in previous studies. The main feature of the new constraint qualification and related optimality conditions is the fact that they depend on individual elements of quasidifferentials of the objective function and constraints and are not invariant with respect to the choice of quasidifferentials. To illustrate the theoretical results, we present two simple examples in which optimality conditions in terms of various subdifferentials (in fact, any outer semicontinuous/limiting subdifferential) are satisfied at a nonoptimal point, while the optimality conditions obtained in this paper do not hold true at this point; that is, optimality conditions in terms of quasidifferentials, unlike the ones in terms of subdifferentials, detect the nonoptimality of this point.

中文翻译：

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基于拟微分的非光滑数学规划问题的一个新的约束限定和尖锐的最优性条件

SIAM优化杂志，第30卷，第3期，第2603-2627页，2020年1月。
本文致力于在最小可能假设下，用Demyanov-Rubinov-Polyakova拟微分方程分析具有相等和不等式约束的非光滑数学规划问题的新约束条件和最强的现有最优条件。为此，我们使用新的约束限定条件，对由准可区分的等式和不等式约束定义的集合，获得了条件子锥的凸子锥的新颖描述。我们利用这种描述和约束条件，在比以前的研究更少的限制性假设下，以拟微分派生了非光滑数学规划问题的最强现有最优条件。新约束条件和相关最优条件的主要特征是，它们取决于目标函数和约束的拟差分量的各个元素，并且对于拟差分量的选择不是不变的。为了说明理论结果，我们给出两个简单的示例，其中在一个非最优点上满足了各种次微分（实际上是任何外部半连续/极限次微分）的最优条件，而本文获得的最优条件不成立这一点; 也就是说，以准微分的最优条件不同于以亚微分的最优条件，它可以检测到这一点的非最优性。