SIAM Journal on Optimization, Volume 31, Issue 1, Page 569-603, January 2021.
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on completeness and limiting procedures. The main attention is paid to generalized derivatives and subdifferentials of the Dini--Hadamard type with the usage of mild qualification conditions revolving around metric subregularity. In this way we develop calculus rules of generalized differentiation in normed spaces without imposing restrictive normal compactness assumptions and the like and then apply them to general problems of constrained optimization. Most of the obtained results are new even in finite dimensions. Finally, we derive refined necessary optimality conditions for nonconvex problems of semi-infinite and semidefinite programming.

中文翻译：

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赋范空间中的变分分析及其在约束优化中的应用

SIAM优化杂志，第31卷，第1期，第569-603页，2021年1月。
本文致力于变分分析的广义微分理论的发展和应用，它使我们能够在不完整的规范空间中工作，而无需采用基于完整性和限制程序的常规变分技术。主要关注Dini-Hadamard类型的广义导数和次微分，其中使用适度的资格条件围绕度量次正则性。这样，我们在不施加限制性正态紧致性假设等的情况下，在范数空间中开发了广义微分的演算规则，然后将其应用于约束优化的一般问题。即使在有限的尺寸下，大多数获得的结果也是新的。最后，