Minimization of semicoercive functions: a generalization of Fichera’s existence theorem for the Signorini problem

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• 作者：Gianpietro Del Piero
• 关键词：Convex optimization ; Noncoercive variational problems ; Signorini problem ; Fichera theorem ; Motzkin decomposition
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1-2
• 页码：5-17
• 全文大小：484 KB
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• 作者单位：Gianpietro Del Piero (1) (2)
  
  1. Dipartimento di Ingegneria, Università di Ferrara, Ferrara, Italy
  2. International Research Center M&MoCS, Cisterna di Latina, Italy
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Engineering Thermodynamics and Transport Phenomena
  Mechanics, Fluids and Thermodynamics
  Structural Materials
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0959

文摘

The existence theorem of Fichera for the minimum problem of semicoercive quadratic functions in a Hilbert space is extended to a more general class of convex and lower semicontinuous functions. For unbounded domains, the behavior at infinity is controlled by a lemma which states that every unbounded sequence with bounded energy has a subsequence whose directions converge to a direction of recession of the function. Thanks to this result, semicoerciveness plus the assumption that the effective domain is boundedly generated, that is, admits a Motzkin decomposition, become sufficient conditions for existence. In particular, for functions with a smooth quadratic part, a generalization of the existence condition given by Fichera’s theorem is proved. Keywords Convex optimization Noncoercive variational problems Signorini problem Fichera theorem Motzkin decomposition