论文标题
在规范空间中具有限制优化的应用的变异分析
Variational analysis in normed Spaces with applications to constrained optimization
论文作者
论文摘要
本文致力于开发和应用一般的变分分析差异理论，该理论使我们能够在不完整的规范空间中工作，而无需基于完整性和限制程序采用常规变分技术。主要注意力是对DINI-HADAMARD类型的普遍衍生物和细分定量的，其使用围绕度量次级的轻度资格条件使用。通过这种方式，我们制定了在规范空间中广义分化的计算规则，而不会施加限制性的正常紧凑性假设等，然后将其应用于受约束优化的一般问题。即使在有限维度中，大多数获得的结果也是新的。最后，我们得出了精致的最佳条件，以解决半无限和半决赛编程的非凸问题。
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 revolved 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.
