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About a special class of nonconvex optimization problems. (English) Zbl 0718.90074
The paper deals with nonconvex optimization problems, the set of feasible solutions of which is the intersection of a polyhedral cone with a hypersphere. Such a set is called spherical polyhedron and it is obviously a nonconvex set. The objective function of the problem is such a nonconvex function whose set of optimal solutions is a closure of a face of the spherical polyhedron. Such problems have similar properties as the classical linear programming problems. An optimality criterion is derived and an idea how to solve such problems is suggested. Some applications are briefly mentioned.
MSC:
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
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References:
[1] F. Nožička L. Grygarová K. Lommatzsch: Geometrie konvexer Mengen und konvexe Analysis. Akademie-Verlag, Berlin. 1988.
[2] F. Nožička J. Guddat H. Hollatz B. Bank: Theorie der linearen parametrischen Optimierung. Akademie-Verlag, Berlin. 1974. · Zbl 0284.90053
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