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Journal of Convex Analysis, Vol. 4, No. 2, pp. 281-287 (1997)
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A Generalization of the Quasiconvex Optimization Problem

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J. M. Gutiérrez

Facultad de Econom\'{\char'20}a y Empresa, Universidad de Salamanca, 37008 Salamanca, Spain, jmgut@gugu.usal.es

**Abstract:** In this paper the quasiconvex minimization problem is included in a problem defined by sets (instead of functions). Lagrangian conditions for both problems are then studied and related. Lagrangian conditions for the standard convex minimization problem are usually defined in terms of subdifferentials. Lagrangian conditions are defined here in terms of those functionals on the set of (quasi) convex functions which satisfy certain axioms.

Constraint qualifications valid at all points in the feasible set are also considered, in connection with questions of redundancy.

**Classification (MSC2000):** 90C30; 49K27,26B25

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