A generalization of the quasiconvex optimization problem. (English) Zbl 0889.90131

Summary: 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 convex 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.


90C30 Nonlinear programming
49K27 Optimality conditions for problems in abstract spaces
26B25 Convexity of real functions of several variables, generalizations
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