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Some transformation techniques in global optimization. (English) Zbl 1100.90037
Liberti, Leo et al., Global optimization. From theory to implementation. New York, NY: Springer (ISBN 0-387-28260-2/hbk). Nonconvex Optimization and Its Applications 84, 45-74 (2006).
Summary: Some transformation techniques, useful in deterministic global optimization, are discussed. With the given techniques, a general class of nonconvex MINLP (mixed integer nonlinear programming) problems can be solved to global optimality. The transformations can be applied to signomial functions and the feasible region of the original problem can be convexified and overestimated by the transformations. The global optimal solution of the original nonconvex problem can be found by solving a sequence of convexified MINLP sub-problems. In each such iteration a part of the infeasible region is cut off and the algorithm terminates when a solution point is sufficiently close to or within the feasible region of the original problem. The principles behind the algorithm are given in this chapter and numerical examples are used to illustrate how the global optimal solution is obtained with the algorithm.
For the entire collection see [Zbl 1087.90005].

MSC:
90C26 Nonconvex programming, global optimization
90C11 Mixed integer programming
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