Titlebook: Global Optimization; Deterministic Approa Reiner Horst,Hoang Tuy Book 19901st edition Springer-Verlag Berlin Heidelberg 1990 Decision Theor

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Elavarasi Pichai,Mageshwaran LakshmananA widely used method to solve various kinds of difficult optimization problems is called branch and bound. In this technique, the feasible set is relaxed and subsequently split into parts (branching) over which lower (and often also upper) bounds of the objective function value can be determined (bounding).

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Outer ApproximationOuter approximation of the feasible set by a sequence of simpler relaxed sets is a basic method in many fields of optimization. In this technique, the current approximating set is improved by a suitable additional constraint (a cut).

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Branch and BoundA widely used method to solve various kinds of difficult optimization problems is called branch and bound. In this technique, the feasible set is relaxed and subsequently split into parts (branching) over which lower (and often also upper) bounds of the objective function value can be determined (bounding).

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Cutting MethodsIn this chapter we discuss some basic cutting plane methods for concave minimization. These include concavity cuts and related cuts, facial cuts, cut and split procedures and a discussion of how to generate deep cuts. The important special case of concave quadratic objective functions is treated in some detail.

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Successive Approximation MethodsIn the cutting plane methods discussed in the previous chapter, the feasible domain is reduced at each step by cutting off a feasible portion that is known to contain no better solution than the current best solution.