English
资源说明：Accurate modelling of real-world problems often requires nonconvex terms to be introduced in the
model, either in the objective function or in the constraints. Nonconvex programming is one of the
hardest fields of optimization, presenting many challenges in both practical and theoretical aspects.
The presence of multiple local minima calls for the application of global optimization techniques.
This paper is a mini-course about global optimization techniques in nonconvex programming; it deals
with some theoretical aspects of nonlinear programming as well as with some of the current state-
of-the-art algorithms in global optimization. The syllabus is as follows. Some examples of Nonlinear
Programming Problems (NLPs). General description of two-phase algorithms. Local optimization
of NLPs: derivation of KKT conditions. Short notes about stochastic global multistart algorithms
with a concrete example (SobolOpt). In-depth study of a deterministic spatial Branch-and-Bound
algorithm, and convex relaxation of an NLP. Latest advances in bilinear programming: the theory of
reduction constraints.
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