Burer, S and Letchford, Adam (2012) Non-convex mixed-integer nonlinear programming: a survey. Surveys in Operations Research and Management Science, 17 (2). pp. 97-106. ISSN 1876-7354
A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, however, things become much more difficult, since then even the continuous relaxation is a global optimisation problem. We survey the literature on non-convex MINLP, discussing applications, algorithms and software. Special attention is paid to the case in which the objective and constraint functions are quadratic.
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