Set containment characterization with strict and weak quasiconvex inequalities

Authors:
Satoshi Suzuki
Affiliations:
Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue, Shimane, Japan
Venue:
Journal of Global Optimization
Year:
2010

Citing 6
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Abstract

Dual characterizations of the containment of a convex set, defined by infinite quasiconvex constraints, in an evenly convex set, and in a reverse convex set, defined by infinite quasiconvex constraints, are provided. Notions of quasiconjugate for quasiconvex functions, 驴-quasiconjugate and 驴-semiconjugate, play important roles to derive the characterizations of the set containments.