Semi-invex functions and their subdifferentials. (English) Zbl 0894.90119

Summary: We introduce the notion of semi-invex function (non-smooth) and the associated subdifferential. We study their properties and establish the conditions for optimality in constrained and unconstrained minimization problems.


90C25 Convex programming
49J52 Nonsmooth analysis
90C30 Nonlinear programming
Full Text: DOI


[1] DOI: 10.1080/02331939108843677 · Zbl 0777.49018
[2] Rockafellar, Convex analysis (1970) · Zbl 0932.90001
[3] DOI: 10.1080/02331939108843693 · Zbl 0731.26009
[4] Clarke, Optimization and nonsmooth analysis (1983)
[5] DOI: 10.1006/jmaa.1995.1057 · Zbl 0831.90097
[6] DOI: 10.1016/0022-247X(81)90123-2 · Zbl 0463.90080
[7] DOI: 10.1080/02331938608843097 · Zbl 0591.49016
[8] DOI: 10.1016/0022-1236(78)90030-7 · Zbl 0404.90078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.