Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives

Author:

Khanh Pham DuyORCID,Phat Vo ThanhORCID

Funder

National Foundation for Science and Technology Development

Fondo Nacional de Desarrollo Cientìfico y Tecnológico

Comisión Nacional de Investigación Cientìfica y Tecnológica

Publisher

Springer Science and Business Media LLC

Subject

Control and Optimization

Reference25 articles.

1. Aussel, D., Corvellec, J.N., Lassonde, M.: Subdifferential characterization of quasiconvexity and convexity. J. Convex Anal. 1, 195–201 (1994)

2. Aussel, D.: Subdifferential properties of quasiconvex and pseudoconvex functions: unified approach. J. Optim. Theory Appl. 97, 29–45 (1998)

3. Avriel, M.: r-Convex functions. Math. Program. 2, 309–323 (1972)

4. Avriel, M., Diewert, W.E., Schaible, S., Zang, I.: Generalized Concavity, Mathematical Concepts and Methods in Science and Engineering, vol. 36. Plenum Press, New York (1988)

5. Barron, E.N., Goebel, R., Jensen, R.R.: The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions. Discrete Contin. Dyn. Syst. Ser. B 17, 1693–1706 (2012)

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