Abstract
The concept of global optimum is discussed versus that of local optimum. Many functions encountered in the applications possess multiple local minimizers (or maximizers) with distinct function values. Finding the global minimizer (or global maximixer) in such cases is often of considerable interest and at the same time a great challenge. Fortunately, most global optimization problems of practical interest fall into two basic classes: dc optimization, which deals with problems described by dc functions, and monotonic optimization, which is concerned with problems described by functions representable as differences of increasing functions. The study of these two basic classes of problems is the main theme of modern deterministic global optimization.
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Notes
- 1.
Unfortunately, such linear programs disguised in “nonlinear” global optimization problems have been and still are sometimes used for “testing” global optimization algorithms.
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Tuy, H. (2016). Motivation and Overview. In: Convex Analysis and Global Optimization. Springer Optimization and Its Applications, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-31484-6_5
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