Outer approximation by polyhedral convex sets

SummaryThis paper deals with outer approximation methods for solving possibly multiextremal global optimization problems. A general theorem on convergence is presented and new classes of outer approximation methods using polyhedral convex sets are derived. The underlying theory is then related to the cut map-separator theory of Eaves and Zangwill. Two constraint dropping strategies are deduced.ZusammenfassungDiese Arbeit befaßt sich mit äußeren Approximationsverfahren zur Lösung von möglicherweise multiextremalen globalen Optimierungsproblemen. Ein allgemeiner Konvergenzsatz wird vorgestellt, aus dem sich neue Klassen von Schnittebenenverfahren ableiten lassen. Schließlich wird die dargestellte Theorie in Bezug gesetzt zur Schnittabbildung-Separatoren-Theorie von Eaves und Zangwill. Zwei Strategien zur Reduzierung der Nebenbedingungen werden vorgestellt.

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