Subdifferential calculus for a quasiconvex function with generator

• Suzuki, Satoshi

• Kuroiwa, Daishi

Abstract

Recently, we discussed optimality conditions for quasiconvex programming by introducing ‘Q-subdifferential’, which is a notion of differential of quasiconvex functions. In this paper, we investigate basic and fundamental properties of the Q-subdifferential. Especially, we show results of a chain rule for composition with non-decreasing functions, monotonicity of the Qsubdifferential, mean-value theorem, a sufficient condition for a global minimizer for quasiconvex programming, and the calculus of the Q-subdifferential of the supremum of quasiconvex functions.

Journal

• Journal of Mathematical Analysis and Applications

  Journal of Mathematical Analysis and Applications 384 (2), 677-682, 2011-12-15

  Elsevier

Keywords

• quasiconvex function
• subdifferential
• monotonicity
• mean-value theorem

Details

• CRID: 1050845763416139008
• NII Article ID: 120005647347
• NII Book ID: AA00252847
• ISSN: 0022247X
• Web Site: http://ir.lib.shimane-u.ac.jp/31349
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles